The Sharks are a gang which have a boat with their name on it. There are four current members of the gang, which include Sharkface (leader of gang), Lonnie (gang member), Ronnie (gang member), Donnie (gang member), and later SpongeBob. It was revealed that there was a fifth member named Jonnie. SpongeBob later replaces him.
Not much is known about the Sharks' past. At some point in time, the Sharks and the rivaling gang, the Pods, had a dispute with each other, which carried over to the end of the episode, where it is revealed that the two gangs are dancing troupes, and, to SpongeBob's amazement, are not actually going to have a fight.
It is also hinted that, at another dance-off outside of the episode, the Sharks were either going up against or just witnessing Bikini Bottom's Internal Affairs as they danced. This hint is given when Sharkface admits defeat, saying "It's over. Nobody beats the Internal Affairs."
The group is most likely a reference to the group "The Greasers" in the 1983 film The Outsiders.