The Right Hand of Doom is almost indestructible and does not experience any pain. It is not clear exactly how strong it is, but an important part of the lore is that it can be used to end the world which does say imply it is powerful. The Right Hand of Doom can release the Ogdru Jahad, forces that will lead to the end of the world.
In the film, this is done by using the hand to reach into a notch in an obelisk and turning the hand like a key. The arm can also be used to punch out immaterial beings such as ghosts. Hellboy alleges that it is useful for opening cans of tuna and winning arm wrestles.
It is also implied that Hellboy’s right hand doesn’t even need to be attached to him in order to wield its power though it will become useless if he dies while it is attached to him.