fb basically means facebook. facebook is a communication networking site. you have to be 14 or over to have an account.
it stands for Finley Breese
It can be an acronym for Facebook, Fantasy Football or Dungeon: aka Fuben, Fire Ball or First Battle(from the MMORPG Perfect World)
There are other uses for computers besides going online, and there are other ways to use the Internet beside computers -- smartphones, for example.
Addict is right.