Divisions reflect your performance in Battles.
There are 11 Divisions in total. You start in the Rookie Division, but quickly move up to Division 10. The highest Division is Division 1.
Higher divisions raise your Point Limits and let you earn more Victory Points and Combat Points from each Battle. As a result, you can get new Crates more quickly.
Gold Crates can contain:
Silver Crates can contain Tournament Tickets in addition to all of the above.
Your current Division is determined by the number of Ranking Points you have.
You can be demoted to a lower Division if you lose Ranking Points in Battles.