On one of my questions I see a "start a bounty" button. What does it mean and what is its purpose?
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From the SO FAQ
When you start a bounty on your question, you're announcing that you'll pay so-and-so rep to whoever fixes your problem within 7 days.
Recently, the bounty system was updated so that you can use it to give extra points to any worthy answer.
The 'start a bounty' button opens the bounty creation interface. It's safe to click on it, there's another button inside which actually starts the bounty.
(Details on bounty -> FAQ or the other answer)