I once swam across a puddle of poop, yeah.. so quit bragging about your shitty endurance! He-heh.. Get it?
Swim is a skill that allows you to do just that, swim. It is based on endurance, your ability to... well, endure the rigors of swimming. The higher your skill level the better your chances are of crossing a body of water without sinking and dying. You also swim faster the higher the skill is. Your swimming is also effected by the weight of the items in your inventory, the more weight you carry the more likely you are to sink/swim slow. You can learn swimming from Smokey in Eschaton Outfitters, marked as EO, in Freedom City.
The shores of North Beach is a good place to train swim; as long as you don't stray more than one block into the sea, you will not sink. Just don't go swimming alone at night, as there's dangers afoot there then.