Question

What is a Wonder Launcher battle?

Answer 1

>From Bulbapedia, the community-driven Pokémon encyclopedia.
The Wonder Launcher (Japanese: ミラクルシューター Miracle Shooter) is a multiplayer battle feature only in Generation V. During a multiplayer battle, if both players have the Wonder Launcher enabled, they will be able to purchase the use of certain items using points that are accumulated each turn.
During Wonder Launcher battles, the player characters have alternate sprites. The Wonder Launcher itself is something worn around the wrist, similar to the Fine Styler, and that shoots items at a Pokémon during battle.

Its makes it able to buy items in middle of a battle with the points you gather from each turn

Hope I helped! :D

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Answer 2

The Wonder Launcher is a multiplayer battle feature only in Generation V. During a multiplayer battle, if both players have the Wonder Launcher enabled, they will be able to purchase the use of certain items using points that are accumulated each turn.

Items available.

So, essentially, it is a battle where you don't use items in your bag, but end up "launching" items such as X-Attack or Potions using accumulated points.