Crazy Hand is Master Hand's crazy twin brother, who unlike Master Hand, acts very insane and goes very crazy with his fighting (hence his name), which is powerful enough to lay waste to half of Hyrule Castle. He is slightly less smart that his twin counterpart. Whenever he keeps laughing and won't stop, his brother Master Hand has to yell at him, "SHUT UP, NOW!" Not that he does.
Crazy Hand often terrorizes villages for the sake of it. The thing is, he's only a hand, so people just step on him, and he is smushed.
Crazy Hand is crazy. Of course, you should know that by now.