If you want to know what the league bonus is for in Clash of Clans, then you should read this next.
Trophy League Bonus or Star Bonus is a reward that is assigned to the winners of 5 stars in their attacks in multiplayer mode. So answering the question what is this bonus for: Prize.
It is an amount of gold, elixir and dark elixir that depends on the league you belong to. Remember that there are different leagues such as the bronze league for rookies, the crystal league, the silver league, the master league, the titan league, etc.
You cannot earn more than one Star Bonus in any 24-hour period.
On the button itself ATTACK the stars made and pending are indicated to obtain the stellar bonus when it is available.