Trophies are tokens of victory that show your rate of success in Raid battles. You gain Trophies by winning Raids, and lose them if you are defeated or if another player Raids you while you are away from the game.
Trophies cannot be consumed or exchanged for any items or Heroes and do not affect your performance in battle. They are, however, used to help find more suitable opponents in Raids - you face players with a similar amount of Trophies as you on a corresponding Raid Arena. More on Raid Arenas here. https://support.smallgiantgames.com/hc/en-us/articles/360001351634-What-are-Raid-Arenas-
The combined amount of an Alliance’s members’ Trophies is used in calculating an Alliance Score. Some Alliances set limits for the minimum amount of Trophies their members may have to not make their Alliance Score drop.
The players with the highest amount of Trophies can be seen at the top of the Global Leaderboards.