To Go Buy A Drink means to stop cockblocking, essentially leaving your friend and the girl alone. It is expected that you will do this without being told, but it is often the case that your friend will say "go buy a drink", at which point you must vacate the premises.
Guy talking to girl: Hey, I really like your outfit today!
Guy's Friend: Yeah it looks nice
Girl: Aww thanks!
Guy to friend: Hey man, can you go buy a drink or something?
Example 2
Guy: Hey man, I'm going to go talk to that cute girl over there.
Friend: Alright I'll go buy a drink
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