Team Battle is a brand new mode accessible in the game's Single, Local, & Wireless battle modes, as well as the Daily Challenges. This mode is a battle where each player selects three Pokémon to use, then selecting the Pokémon you wish to start with using a button prompt. There, the first player to knock out all three of their opponent's Pokémon wins the match. However, it is not as simple as it seems.
Any damage you take within the Team Battle round carries over to the next round after a little HP recovery, so if you won a match with 5 Hit Points, you'll continue forwards on low Hit Points rather than have a full recovery.
Team Battles are also good to use in order to increase your Pokémon's Skill Level.