There are five leagues in the Arena: Bronze, Silver, Gold, Diamond and Champion. Higher leagues have greater rewards!
When a league week starts, all players are placed into leagues based on their final Trophy score at the end of the previous week. If your Trophy score is below the limit of your league at the end of the week, you will move down to a lower league.
At the start of every Arena League week your Trophy score will be set to the limit for the division, this is why your score usually drops when you're promoted to a new league!