Scrooge has already told Marley that he doesn't really believe his senses because "'A slight disorder of the stomach makes them cheats.'" In other words, Scrooge thinks that Marley is just a trick of his imagination, a minor hallucination caused by having eaten something either spoiled or not fully cooked. Scrooge even makes a joke at Marley's expense when he says, "'There's more of gravy than of grave about you, whatever you are!'" He employs a pun, a play on the words gravy and grave because they sound so much alike, and Scrooge means that Marley's appearance has more to do with something he ate than it does with death. When Scrooge finally calls Marley a "'humbug!'" Marley loses all patience.
At this the spirit raised a frightful cry, and shook its chain with such a dismal and appalling noise, that Scrooge held on tight to his chair, to save himself from falling in a swoon. But how much greater was his horror, when the phantom taking off the bandage round its head, as if it were too warm to wear in-doors, its lower jaw dropped down upon its breast!
Marley unties the bandage around his head, a wrapper that is meant to keep his jaw closed in death, in order to terrify Scrooge into a belief in him. If Scrooge refuses to believe in Marley, then the ghost(s) will have no effect upon his chances for salvation. Marley's jaw falls to his chest because he has been dead for some time and so, theoretically, the muscles that would allow him to be able to hold his jaw closed would have lost their integrity. In order to convince Scrooge of his reality, Marley allows himself to appear frighteningly dead, a real corpse, in this moment, so as to impress upon his old friend the seriousness of the situation.