Influence, as with persons able to grant favors. An advantage over another or others.
Clubber #1: Yo, can you get us to the front of this whack ass line.
Clubber #2: Fuck dude, I don't got pull at this club.
Clubber #1: I thought you had pull all around town.
Clubber #2: Yeah but this place is new, I haven't had the chance to soften up the owner yet.
Clubber #1: Aw shit.