Mystery Boxes are a wildcard gameplay mechanic that provide fun rewards for players and their teams. These rewards can range from huge points multipliers that can drastically increase a team's points, to random gifts like NFTs and special event access, and also special airdrops of $ME3 tokens.
You can earn Mystery Boxes to open every time that you complete Social Actions in Hype Pool, with points granted to your team immediately, and other rewards granted at the end of the weekly game. You can learn more about Game Rewards in the dedicated help article.