The Paralyzer is Zero Suit Samus' Standard Special Move. Its main purpose is to stun opponents, but it also deals some damage. It can also be charged to increase the time an opponent is stunned.
The Paralyzer is also used as her down smash, apparently with a similar effect (although fired downwards).
Interestingly, the stunning effect caused by the Paralyzer is not affected by knockback resistance. This means that it can even stun bosses.
In Metroid: Zero Mission, Zero Suit Samus' part of the game is primarily a stealth game, even with a charge shot, the best she can do with her gun is paralyze Space Pirates for a few seconds.