Buying the button in poker means posting the big and the small blind at once in order to participate in the hand if you are new to the table or have missed the blinds for some reason. This only applies in cash games.
Buy the Button Poker Example:
Let’s say that you briefly stepped away from the table, and when you come back, you see that you’ve missed the big and small blind. If you still want to play that hand, you’ll have to “buy the button” and post the owed big and small blind. Otherwise, you will have to skip some hands and wait until you are in the BB seat to actually participate.