Well, what sort of stars are you talking about? I'll assume you don't mean the thousands of tiny points of light up in the night sky...
There are two places in the Advance Generation where Stars appear, that you might not understand about. First, they are part of the grading system in Pokémon Contests, introduced in Ruby/Sapphire. These work like dog shows and whatnot; instead of their battle prowess, pokémon compete in breeding categories such as beauty and intelligence. There are two rounds of judging; the first, a simple popularity vote, is tallied at the end with stars; the better you did, the more stars you get. The results of the second round, in which the pokémon use their four moves as 'appeals', are tallied with hearts.
Second, one of the features added on to the new spiffy 'Trainer Card' are Trainer Stars. You get stars on your trainer card for completing challenges; for example, you get one for becoming the Pokémon League Champion and another for completing the Pokédex. There are four Trainer Stars to earn in each game Version.