What is it?
Proof that drugs were involved in the making of BioShock. How else to explain the strange and incredibly surreal ability to call forth an army of angry bees and send them swarming at your enemies' heads? From within the flesh of your own arm, no less.
When should I use it?
When you don't have the time or concentration for anything else. Precise aiming is awfully difficult when creatures are bashing your face in from all sides, something the Splicers and Big Daddies are awfully fond of doing. With the special exception of Electro Bolt in water and Incinerate on oil, Insect Swarm is the only plasmid that can harm multiple enemies at once. Don't worry about lining up a shot - just unleash the cloud of poisoned stingers as fast as possible.
Insect Swarm, like many plasmids, is only a short-term solution. The bees take awhile to finish monsters off, so you'll want to fire other weapons in the meantime. Oh, and stay away from the buzzing chaos. You're as likely to get stung as everyone else.
Does it work against a Big Daddy?
The bees will bother a Big Daddy for the same amount of time they do regular enemies, and nothing's funnier than watching a guy in a giant diving suit swat blindly at teensy tiny insects. Like Incinerate, however, Insect Swarm will only make him angrier at you.
If you have enough Eve, the game's equivalent of mana, feel free to pile on more and more bees. But if you run out and he's still not dead, you'd best run or have a Plan B ready.