The Invincible Star, aka the Starman, Invincibility Star, and like names, is a power-up found in games in the Super Mario Brothers franchise of games, as well as in related franchises.
The invincibility star is, as the name suggests, a star (of the traditional five pointed iconographic variety) that grants invincibility, for a short period of time. Such invincibility is displayed by rapidly palette swapping Mario (and/or Luigi), and it is one of three power-ups found in the original game. For reasons that are doubtlessly lost in the murky depths of video game history, the Invincible Star does not emerge from a standard Question Mark Block, but only from a standard brick block.
The Invincible Star is not a highly useful power-up overall, although this depends on the game and situation. Although the game designers might not have realized it while designing the game, the enemies in a Super Mario Brothers game are fairly predictable and usually not challenging, with the largest challenge in the game usually coming from jumping and avoiding pits. Since the Invincible Star does not protect from this, its utility is somewhat limited.
On the other hand, whatever the utility, how can you refuse a star with two small, pixelated, but deeply emotive of the desire to help you in your time of need, eyes? And having theme music that speaks of your excellation, even if only for several measures?