The Arena is used for player vs. player combat in Star Trek Timelines.
Each division has its own leader board and potentially daily rewards (schematics for certain ships), with more valuable rewards available to the higher divisions.
Once you choose a division, you are then prompted to choose your ship and crew. When you have done that, you can then choose between three other players to battle. Their rank in the leaderboard, ship abilities and crew, and basic ship stats are available to view.