Bounty Boards are boards where you can pick up and turn in Bounties. They can be found throughout the world (as long as village generation is turned on in the config), or they can be crafted.
The objectives and rewards that show up at a Bounty Board are themed based on an item called a Decree. Every Board starts with it's own Decree, and up to three Decrees can fit on a Board at once.
One thing to note is that everyone 'sees' the same Bounties when viewing the inventory of a Bounty Board. However, players 'see' their own copy of the board's inventory. This means that you can take a Bounty from the Board and it won't disappear from your friend's board. This means that if you see a particularly good bounty, you can tell your friends so that they can pick up their own copy!