Tribute is a mechanic on certain creatures that gives your opponent a choice when the creature enters the battlefield. Each tribute creature has a number, and as it enters, an opponent decides whether to put that many +1/+1 counters on it (paying the tribute) or let it enter without those counters—in which case a different, usually nastier, ability triggers. You're essentially offering a "lesser of two evils" decision to the opponent.
The nuance people miss: the opponent chooses, not you, and the "tribute not paid" ability only happens if they decline the counters. The creature's printed power/toughness already assumes tribute wasn't paid, so paying tribute makes it bigger.
In Commander, the opponent to your left typically decides, but technically you choose which opponent makes the call. With multiple opponents, this adds a fun political layer—one player decides which downside your whole table faces.