Stars are a fundamental element in Diamond Digger Saga. They are present on all levels. For each level, stars can be earned by reaching certain score requirements - in other words, by reaching certain amount of points. A player can earn up to 3 stars per level.
By reaching the level score requirement, a player earns one star. Afterwards, a player has to earn certain additional amount of points in order to gain either 2 stars, or 3 stars. The number of stars earned depend on the score at the end of the level. You figure out when you achieved the first star as Diggy says: Wheeew!