We keep your Discord ID and display name, your email if you sign in that way, the game-account specs you enter (furnace level, troop tiers, and similar), and the applications you submit for events.
It's used to run alliance operations and place people into events — rosters, documents, and schedules. We don't advertise with it and we don't sell it.
Ask a leader and they can remove your data. If your account is deleted, applications already submitted stay linked to the game account they were made for, not to you personally, unless you ask for those to be removed too.