First, some definitions:
The Primary Investigator (aka the PI)- The head of the laboratory. He is a professor, faculty member, and mentor to his post docs and students.
PhD (aka Doctor of Philosophy) - An advanced academic degree, usually given in the sciences or humanities. Often has a research focus.
Qualifying Exam (aka Quals, Prelims, Comps) - An exam given to PhD candidates which determines if they are competent to pursue the remainder of their thesis.
Graduate School in the Sciences - Basically, if someone wants to do any kind of scientific research; biomedicine, chemistry, physics, cell biology, biochemistry, etc., one needs a graduate degree in one of these fields. For simplicity, I will focus on the biological sciences I am most familiar with that area. This would include biology as well as areas like biochemistry, cell biology, biophysics, molecular biology, and microbiology. There is a ton of overlap in these fields, so avoid getting bogged down in the details of the names. There are a few programs around the country which give out masters degrees in hard sciences, but not many. This is typically not thought of as all that useful for someone who wants to do their own research down the line (it can be useful for someone going into industry, because they might be in a more business oriented job that requires some science background). For the most part, when someone gets an undergraduate degree in science, and they are interested in pursuing research as a career, they apply to PhD programs. Most universities have a separate PhD program for each department.
PhD Programs - The best thing about these typed of programs is that they pay you to attend. Typically, they give all of their students a yearly stipend which can run between $18,000 and $25,000. Not much but it's enough to get by on for 5 or 6 years, while you are in your early to late 20's. This is the typical length of time that you would spend in grad school. Often the first 2 years are spent taking classes. In the first year we do rotations along with classes. Rotations are essentially try-outs for a few labs at the university to see which type of research we want to go into. It's both a try-out from the PI's perspective (do we fit in with the lab?) as well as from ours (is this the type of lab we want to be in?). In the second year, we have decided which lab we want to work in, but are still taking classes (this can vary depending on the program). At the end of our second year, most programs require us to take some sort of right-of-passage test, often called a qualifying exam (or qual, see definitions). The format of this can vary from a multiple choice exam, to an oral exam, to a more research oriented oral presentation. It is however, extremely stressful and can be quite difficult. It essentially determines whether the program believes that you are good enough and smart enough to continue with a thesis in their department. If you fail, which happens with surprising frequency (again, depending on the place), the department will often give you a masters degree and send you on your way. This, I believe, is another reason why masters are not particularly useful in the sciences. They are probably thought of as someone failing to get a PhD, rather than someone achieving a masters (not to knock anyone with one, just my observation). Anyway, once you pass your qual you are ready to working towards your thesis.
The Thesis - Actually, by the time the end of your second year rolls around you have probably already figured out what you want to work on, and it will typically take another 3 to 4 years in order to accumulate enough information to be considered worthy of a thesis. The term thesis itself has several meanings. It is the central argument of a paper or proposition. It is also the name for the physical document which is the summation of your 5-6 years of graduate work (this definition is interchangeable with dissertation). So there is some understandable confusion when someone says "I'm in grad school working on my thesis". Typically this is not what a person who is, at that time, writing their actual thesis would say (if they were doing that you probably would not see them for several months anyway). What they mean is that they are busily working in the lab to accrue enough data to support their thesis. Usually a student is required to propose their idea for a thesis topic (called a thesis proposal) around the beginning of his/her 3rd year, after qualifying for continuing her/his education. The student must select a few faculty members to make up his thesis committee. This group will judge the students proposal, determine whether it is a) achievable and b) worthy of a potential thesis, make suggestions and send the student on his/her way. Typically students meet with their committee members yearly, so they can assess the progress and guide them in the right direction. It's a particularly useful part of grad school as the committee members are often very knowledgeable people who are there specifically to help.
As an example, let us say that Jimmy applied and was accepted to the biochemistry department at Cornell University. He spent his first year rotating in 3 different labs, a fly genetics lab, a structural biology lab, and a cell division lab. All the while he was taking classes on Cell Biology, Gene Expression, and Human Genetics. You'll notice that there is a seemingly wide range of fields that Jimmy is learning about. That is typical as even though each of those labs has an area which they specialize in, there are many techniques and principles which would be used in each lab. Additionally, even though Jimmy will choose a fly genetics lab to work in, it behooves him to learn as much as possible because, as we shall see in the post doc section, he will most likely choose to work in an area that differs in some way in the future.
So at the end of his first year Jimmy chose the structural biology lab, and started discussing with the PI what type of research project he is interested in pursuing. Jimmy, it turns out, would like to know the 3-dimensional structure and function of a protein from a bacteria which is involved in infecting humans. The PI and Jimmy plan out a loose course of action for the next several years which will hopefully allow them to understand a significant amount about this protein. If they succeed in shedding light on the details of this protein, JImmy will have enough data to write his thesis, and will have supplied the world with a little bit more information about a disease causing bacteria. Not bad, but it's still a long way off. He spends most of his second year toiling away in the lab, trying to work out conditions for isolating large amounts of this protein from the dangerous bacteria, all the while taking another 2 classes in order to fulfill the requirements of his program. By the time spring of his second year rolls around, he realizes that his approach has not worked as well as he had hoped, and he needs to alter his approach. But now his quals are coming up and he has to put everything on hold so that he can study for them. He passes his oral exam, and submits his thesis proposal to the dean of his department which is accepted.
Finishing Grad School - Once the proposal for the thesis has been accepted, the student toils in the lab for another few years. Not to sound self-pitying or anything, but we often work long, painful hours with very few results. We're like baseball players, if we get something to work 3 out of 10 times, we're all-stars. Most of what we try does not work. That's why you have to have a very specific personality to enjoy research. You can't get discouraged, and you can't expect too much. Anyway, this is the time that I find to be the most difficult to explain to non-science people. We are no longer taking classes, but we aren't working at a job. I often interchange work and school when describing what I do. Sometimes I feel as though it is more accurate to say that I have a full-time job, because saying that I'm in school gives the impression that I do nothing except attend classes and study. That's really not the case. I personally work 10+ hours in the lab/day during the week, and another 15 or so on the weekends. Plus I often come in at 3am simply because my experiments don't care what time it is. Add in the reading that I do at home in the evenings and I certainly work more than any non-scientists that I know (except, frustratingly, newly graduated lawyers).
Let us now return to Jimmy's hard-working adventures in crystallographyland. He returns to the lab to rework his approach and gather some data. While he failed in his first year in the lab to purify the protein in any significant amount, it was not a total waste of time. He was able to optimize the conditions of is purification so that, in the end, he had a small amount of highly pure protein. He also was able to clone the gene which encodes for this protein, which meant that he could try and express it in large amounts in some other type of cell. He does this, optimizes things, works long hours in the lab at all times of day, and ultimately gets his hand on large amounts of the desired protein. He crystallizes it and determines the 3-D structure using x-ray diffraction. This takes many months, but in the mean time he has designed an assay for the activity of the protein, and makes several mutants, which in the end reveals how that protein helps the bacteria to infect humans. Overall, this body of work took him 3 years. When he presents it to his thesis committee, along with a paper that he authored and published, they tell him "good job, go write your thesis". He takes another 6 months to write, as well as finishing a few "loose-end" experiments. He submits the thesis to his committee, and prepares his defense. He presents his thesis work in a public lecture and then his committee asks him tough but important questions about his work and what it means. He answers them appropriately, and they award him a PhD. It took 5+ long years, but it was worth it, because now he can go on to a pot doc, which is not exactly a huge change. Wait, that wasn't worth it at all! Jimmy is pissed!
The Post Doc - This term is a shortening of 'Post-doctoral researcher'. So it means someone who has received their PhD is doing some more research. Grad students and post docs work in the same labs, but most often a grad student moves to a new lab upon graduation. Basically, this is an advanced but in-between stage. In grad school we kind of learn how to do research, and many of the underlying principles of research, and a whole lot of background in whatever general field we are entering. When we move on to a post doc, we are essentially thought of as independent researchers who must come up with our own experiments and projects. As with many things in this field, there is not really a clear demarcation in these things. Good grad students who are trained well by their PIs often have the capacity to think creatively about their project, and often times post docs need a little help from their advisors in designing experiments. However, by the time they are finishing in the lab, a post doc should really be quite competent at thinking creatively and critically, and have a good idea of a research project that is heavy enough so that they could start up a lab based around that idea. I think this is the main point of a post doc; to hone one's experimental skills as well as one's publication record enough to where universities will consider you for a faculty position.
Faculty Life -Now, I am nowhere near starting a lab, but even from my distant vantage point it looks like a daunting task. First you have to convince a department at a university that your ideas are original and important enough to warrant a significant chunk of startup money and lab space. Then, if you are fortunate enough to get that, you have to convince the US government (some other grant agency) of the same thing so that they will give you renewable grant money for your research. The odds of getting a position get slimmer and slimmer every year, and the odds of getting both are shrinking to nothing (especially with this administration and their cutting of funding for basic research). But if you are fortunate enough to get those things, you still have to be hard-working and fortunate enough to get enough good results so that your department will grant you tenure. Once tenure is granted, you can finally relax, a little bit anyway. There's a myth that tenured faculty do nothing, but I have never seen a single person stop working once they receive tenure. In fact, I think that most of the greatest work is done after tenure, possibly because they no longer have pressure to get positive results (except for the pressure to maintain the non-guaranteed grant money will keep coming in). They can move over to some more risky projects which may or may not work, but which are potential home-runs. Anyway, a young PI only has so much time in order to accomplish what is required for tenure. We call this a tenure clock, and it begins ticking the moment he/she sets foot on campus. It's usually somewhere between 5-10 years, but it depends on the institution and their policies. If they do not accomplish enough, their tenure committee will deny them, and their career can be in jeopardy. Often when this happens a PI will move to a smaller university or switch to more teaching duties, or leave academia altogether.
So you can see that academia is a high-risk, low reward type of career. Grad school is long and demanding, but at least they pay for it. Professors don't get paid that much on average, although a tenured professor can make a decent living and the job security is unbeatable. Aside from that, I believe there are 2 reasons for people to enter this line of work:
1) We want to change/save the world. This can be a little misleading, because realistically we are not going to make much of an apparent difference. However, the research that we do can lay the groundwork for more research which can ultimately lead to cures for diseases, or new technology that will better people's lives. This is what we tell ourselves at least.
2) We are insatiably curious and have questions that need answering. This, I would guess, is the most common reason. I often tell people that I am not, by any means, altruistic (so take me out of category 1), I just enjoy science very much, and happen to be pretty good at it. What else can I say?
So if you are a grad student/scientist and have been having trouble explaining to your parents or friends what you do, feel free to pass this along. Also, if there are other areas that could use clarification, I'd be happy to edit this with those in mind.