It's the next logical move in understanding how our genetic material makes us who we are. Having so many genomes sequenced and at our disposal will make it easier for researchers to make confident conclusions about which genes cause certain traits. For example, imagine a researcher comes across a patient with a rare disease, which has not been traced to a particular mutation. All the Dr has to do is sequence the patients genome, then search a database which contains the 1000 genomes to see if there are any patients with the same affliction. If there are, Doc can then align the 2 (or more) genomes and see if any SNP's or haplotypes stand out.
This strikes me as a perfect primer situation. Once these genomes become publicly available, researchers who utilize it can deposit the sequences of their own patient's genome into the database. So the more people utilize it, the more useful it becomes. 1000 sounds like a very reasonable starting point to get people using it. Once enough sequences are deposited, diagnosing genetic disorders will become a thing of ease.
A small technical note, it looks as though they plan on using shared sequences to move the project along quickly. By looking specifically for stretches of DNA that show a lot of variation, they can streamline their efforts. It will be slightly less complete than if they were to sequence the entire genome, but equally useful.
It can be utilized by researchers who are interested in what causes any type of trait, not only diseases (although that's obviously the most useful). Let's say I want to know what gene causes red hair, or an excess of moles on a person's skin. With enough sequences it will become almost trivial. We're not quite there yet, but it is coming soon.