After entering the Hall of Fame, you now have access to the Battle Area. You can sail to it from Snowpoint City. In the Battle Area is the Battle Tower, where many talented trainers from all over the in-game globe gather to test their battle skills. Winning consecutive matches in the Battle Tower grants you battle points (BP), which you can use to exchange for rewards.

Below is the complete list of everything you can purchase from the Battle Tower, including their specific uses, in Brilliant Diamond and Shining Pearl.