Power Stars are items you can collect in SM64. There are 7 power stars in each level (8 in the DS sequel) and some you can get by defeating bosses. They sometimes appear in Super Mario 64 Bloopers but not that often. Apparently they're alive because they have eyes and stuff.
Power Stars are collectible items that can grant Mario access to more levels in-game (like Goal Poles from the original Super Mario Bros. and the New Super Mario Bros. series)
Power Stars in Super Mario 64 and Super Mario 64 DS are scattered throughout the different courses. The Power Stars are usually found in the open or will appear after completing a certain task. Boss enemies will have a Power Star, and collecting eight Red Coins will cause a Power Star to appear at a Star Marker. Collecting one hundred Coins in a course will cause a secret Power Star to appear.