Based on the central character in the Eminem song of the same name, a "stan" is an overzealous maniacal fan for any celebrity or athlete.
A Typical Kobe Bryant Stan would say something like.
"Kobe Bryant scored 81 points last night. Kobe could beat God himself in a game of 1 on 1 hoops. To hell with Michael Jordan or Wilt Chamberlain, they arent on Kobe's level!"