Bounties are randomly generated quests that can be accessed via the Bounty Board in Westmarch. You can complete up to 12 bounties per day, although only 4 at a time are visible on the board. After you finished a bounty and collected its rewards, it will disappear from the board and a new one will take its place. Up to 3 times per day you can reroll any bounty on the board.
After you complete a bounty you can turn it in at Bounty Quartermaster Derek to receive Gold, Experience and Item rewards. If you complete 4, 8 and 12 quests in one day, you get additional rewards. Uncompleted bounties left on the board do not carry over to the next day.
It's also possible to do bounties in groups. When a party leader accepts a bounty it is shared to the group. A party leader can also share bounties by clicking the portrait image of a party member.
Bounties are currently a very valuable resource in Diablo Immortal; they are one of the best ways to farm XP and quickly level up. Their rewards do scale with additional difficulties (Normal, Hell 1, Hell 2).