Power Star

Power Stars, also referred to as Stars, are collectible items introduced in Super Mario 64 that can grant Mario access to more levels in-game, unlike the similar-looking Super Stars, which only give brief invincibility. In Super Mario 64, Super Mario Galaxy, and Super Mario Galaxy 2, when the star for any given level has been collected, playing the level again will turn the Star into a translucent version of itself (similar to how Star Coins work). This Star can be collected, but it will not add to the player's total Star count.

(The above text is from the Super Mario Wiki and is available under a Creative Commons license. Attribution must be provided through a list of authors or a link back to the original article. Source: https://www.mariowiki.com/Power_Star)