A bounty is when a user offers a portion of their reputation to be awarded to an answer on a question. They are used to draw in more attention to post. Use this tag for questions you may have about bounties.
From the Bounty help page:
A bounty is a special reputation award given to answers. It is funded by the personal reputation of the user who offers it, and is non-refundable. If you see a question that has not gotten a satisfactory answer, a bounty may help attract more attention and more answers. Slice off anywhere from +50 to +500 of your own hard-earned reputation, and attach it to any question as a bounty. You do not need to be the asker of the question to offer a bounty on it.
See What is a Bounty? How can I start one? for more information.