After having a host of back and leg issues in 2007, I decided that 2008 was the Year of the Core for me. To that end, I've been taking Exer-ball class and various other "core strengthening" classes.
The reason you need to strengthen your core is that it stabilizes your body. A strong core will protect your back and legs from injury, and it can make you a stronger, faster runner.
Check out Runner's World's anatomy of the core for a cool introduction to the body's core muscles and their main functions.
Running miles will not give you six-pack abs (or I'd have a case by now). It will help keep the jiggle off your core, but it won't firm things up in the mid-section like weight training, crunches, ball workouts and abdominal-targeted exercises will.

