The half-marathon is a footrace just like any other road race (5k, 10k, any-k, really). However, as far as standard road race distances go, it is the last big step before the Marathon.
Needless to say, the half-marathon, or just "the half" as most runners put it, is half the distance of a marathon, leaving it at a still-intimidating 13.1 miles (21,097.5 meters).
Most half-marathons cost a little bit more than the average 10k to enter, and not near as much as most large marathons, so it's a rather popular race as far as "bang for your buck." Also, it's one of the few races that most people who run it aren't specifically training for. That is, most people who are running a half aren't trying to better their time in that race. Usually, it's as part of training for a marathon, or else using it as a fun long run in your training program for a 10k (or 8k for many college students).
However, this casual atmosphere, as well as easy entry and (usually) awesome t-shirts make this a rather enjoyable way to spend your Sunday morning. The race is long enough that you can relax for the first few miles, share some jokes, and not have to worry about wasting energy. You've got another 10 miles to go, after all. A 10k is usually too short and intense for the front-runners to enjoy it. A marathon has the same social opportunities, but the distance is too daunting to allow the average runner less than two months of preparation.
Also, half's are one of the shortest races where water stops are sometimes necessary. Nothing makes you feel more important than there being tables loaded with water and sports drink along the route which you are running.
In conclusion, halfs are awesome. The people who run them are usually in a variety of fitness levels, so there are groups for everyone and a huge number of people at every race.
If you are currently in a running program, I recommend you try one if you haven't already. If you aren't in a running program, you should consider trying to start one. Runners are notoriously helpful and friendly.
Run well!
World Records
Men: Paul Tergat, KEN - Milano April 4, 1998 - 59:17
Women: Elana Meyer, RSA - Tokyo Jan, 15 1999 - 1:06:44