The Alligator is a boss that appears near the end of the sewer section in Resident Evil 2. Through unknown circumstances, a normal sized alligator became infected with the T-Virus and grew enormously. It normally inhabits the garbage dump, where food is most easily available (it's large size also limiting it's movements around the sewer system) and is fond of biting down on anything, edible or not (somewhat akin to the real life Tiger Shark). It attacks the main player during their efforts to retrieve either Sherry Birkin or Ada Wong (depending on the chosen character) crawling out from the garbage dump to chase the player along a tunnel.
Other examples of infected alligators would be seen in both Resident Evil Survivor and Resident Evil Outbreak File #2, although the effects of the T-virus on the later example was strictly limited to increased aggresion.
The Alligator can be killed by simply shooting it, causing it to eventually smash a hole in the wall and escape. Killing it in this way cause a small amount of ammo to appear a little later on. The other more economical method involves releasing an emergency gas canister which the Alligator prompstly picks up in its mouth. When the canister is shot, it explodes taking much of the Alligator's head with it. Killing it this way means it can be killed with 1 hand gun round.