As we know from previous films, Wormtail is the guy who betrayed Harry's parents when they were hiding from Voldemort. He has been helping the Dark Lord ever since, apparently, and in this film he has a hand in bringing Voldemort fully back from the weakened state he's been in for thirteen years.
And we mean it when we say "has a hand"…because he literally chops off his hand as part of the spell/potion prep he uses to bring Voldemort back:
WORMTAIL: Bone of the father, unwillingly given. Flesh of the servant, willingly sacrificed. And blood of the enemy, forcibly taken. The Dark Lord shall rise again.
As a reward for his assistance, Voldemort grows Wormtail a new silver hand pretty much immediately upon returning to full strength. Sure, it's not the same as having his original hand, but…it's good to be appreciated by the sociopath you serve, we suppose?