Power Stars are stars that provide power to Peach's Castle and the Comet Observatory. Each star was originally a Luma. They are found only in Super Mario 64, Super Mario 64 DS, Super Mario Galaxy and Super Mario Galaxy 2, but a similar item, the Shine Sprite, appears in Super Mario Sunshine and is also confused with the smaller version, the Starman.
Super Mario 64 and Super Mario 64 DS
In Super Mario 64, there are 120 Power Stars in all, 7 in each of the game's 15 courses, and the remaining 15 are Castle Secret Stars. Super Mario 64 DS has one more star in each course, and 15 more Castle Secret Stars for a grand total of 150.
They are now used to power the Comet Observatory. In this game, there exist several variations of Power Star: Grand Stars, Green Power Stars, and one Red Power Star. There are a total of 242 Power Stars including the types mentioned above, and including playing through the game again as Luigi.
They are used to power Starship Mario. In this game, there are two variations of Power Star: the Grand Stars and the Green Power Stars. There are 242 Power Stars spread across 6 main Worlds and a Secret World.