You earn stars by clearing levels. For clearing a level you earn one, two or tree stars depending of how high you score. You can see your score at the bottom right corner when you are playing the level at PC or Mac and monitor your progress. The mobile version of the game doesn’t have this feature.
If you have earned one star on a level the first time, you can come back to that level later on and try to earn more stars. Every level with a guide here at the Fan Site have noted how many Points you need to get 1, 2, 3 Stars. You can use the level tags to the left to find your desired level. Or just CLICK THIS LINK to get to the Level index for Bubble Witch Saga.
You can not get even 1 Star at a level, even if you have the score needed, unless you have cleared the ceiling, aka got at least 9 holes up there to break it.
E.g. 70 stars unlock the potion that gives you extra holes in the ceiling and 90 stars gives you an extra heart!!!
There is a separate listing of all known achievements in Bubble Witch Saga.