The Left-Hand of Horror is capable of making anyone's worst nightmare a reality (unless, as revealed by Grim, their worst nightmare is already a reality) in order to test those who approach it. When someone passes the test, they may turn it off or on, and control its powers.
It is known that in an alternate future, the hand was retreived by someone who became known as The Lord of Horror.
The origin of the 'Left-Hand of Horror' occured centuries or millennia before the events of the movie. Horror the Ancient, wanting to rid himself of his fears, got it into his head that in order to do so, he would have to confine all of his fears into a lone body part and then cut it off--and literaly cut himself off from fear. And so, Horror went forward with his plan, magicaly channeled all of his 'fear' into his own left hand and then cut it off at the wrist.
This, however, did not work out as Horror had planned, the act of magicaly channeling so much power in the form of 'fear' into one place, into his left-hand, rendered the hand into an object of awesome power, the 'Left-Hand of Horror' was literally able to bring into life the things that people who would approach the hand fear the most.
On Horror's end of his predicament, the act had not only not rid him of his fears, but had also deprived him of his left-hand--he was a "leftie", and now couldn't even sign his own name--and could not even reclaim it. Since then, now residing on The Isle of Peril, (an island situated in a dangerous section of The River Styx,) Horror was left to stand watch over his 'Object of Power'.
- It's one of the few things that defeated Mandy, and one of the few things to cause her to show fear.