You can earn 1 to 3 stars per cleared level as following your score.
If you clear the level with high score, you will get 3 star and it will gives you more coins as rewards.
Also, you can get additional present when you get many starts on the stage.
But the score standard is different by levels. Even if you clear the mission, you may fail to the level if you don't get one star at the same time. Keep it mind that one start if basic requirement for clearing the level.