Technically it enables exhaust to flow more freely. Usually this translates to a bit less resistance on the motor across the RPM range. Removing the cat will make the bike sound, as described by others, a bit deeper or louder.
I've also heard it described as "raspy" if you don't have a muffler or resonator.
although I'm in California (one of the toughest emissions states) but truthfully, I think there are better ways to get the gains. (Lose 20lbs, airbox/filter, new muffler) The downside of removing the cat is that it leaves exhaust fumes on your clothes. I REALLY don't care too much for that smell, nor the hassle of drilling out the cat and on top of that Catalytic converters from the factory run a couple hundred bucks so it's expensive if you change your mind. The worst part is that the cat is integrated into the header so these two pieces can't be modded independently unless you get some work done on it at an exhaust shop.
Granted, cats on bikes is not as heavily enforced as cars, and only recently have they started putting cats on bikes, but in my opinion it was a good move. At least for me, my bike is plenty fast enough, and I could afford to lose 50 lbs.