MasterHand is essentially the God, the Creator, and the Holy Being of BedrockPerson's videos. He is the representation of real-life Bedrock's right hand (he is right handed). He has appeared in the 50 subs special as well as the movie and some paraphernalia. It's unknown if his twin, Crazy Hand, exists/has a role in the universe.
Master Hand is pretty much exactly what you'd expect. He's a giant hand, strong, and almighty. He controls the universe because again, he's God.
Master Hand can travel through dimensions as well as probably control some sorts of multiversal physics. He runs the overall multiversal as well as work to keep it in balance regardless of the cost.
In his first appearance, The Dimensional Discrepancy, even after defeat Master Hand seems to communicate with bedrockperson via a certain font. Coincidentally, in the Canyouseethewords series, Decay The Witherer uses the exact same font. Decay also uses some of the same phrases (i.e. "Come home")