A Bracket is a block of players whose scores are competing against each other in a PvP event. It divides players into, effectively, separate events, each with their own Rewards tiers. The player blocks are of a size that matches the Rewards structure, and Rewards are the main reason it is necessary.
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Players are entered into a bracket when they tap/click the "Join Event" button on the Activity Hub or Event screen in-game.
Event brackets are generally sized at no larger than 3,000 players, and sometimes smaller.
Ranking for purposes of individual rewards is determined by how a player's score compares to the scores of others in your bracket.
Brackets do not affect matching; a player may have battles against players in other brackets, but their scoring is entered in their separate brackets' score tiers.
When the last bracket is full and another player joins the event, a new bracket is formed with that player in it. Any player joining the event after that is placed into the new bracket.
Sometimes a new bracket is formed very close to the end of an event. In this case it is possible to get high Ranking Rewards without playing the entire event, sometimes without even playing a single fight in the event. This is usually referred to as "Bracket Sniping" and carries significant risk, as it is extremely difficult to meet Progression Rewards, and it requires luck to get into the top of a new Bracket rather than the bottom of an old Bracket.
Sniping became popular, and had its greatest utility, in the Quick Battle event, where the rewards were great, but many battles would be required to gain rewards, without sniping.