What does it mean to “buy the button."?

Answer 1

A rule originating in northern California casinos in games played with blinds, in which a new player sitting down with the button to their right (who would normally be required to sit out a hand as the button passed, then post to come in) may choose to pay the amount of both blinds for this one hand (the amount of the large blind playing as a live blind, and the amount of the small blind as dead money), play this hand, and then receive the button on the next hand as if they had been playing all along. See public cardroom rules

A tactic most often used by late-position players: a raise to encourage the later and button players to fold, thus giving the raiser last position in subsequent betting rounds.