From Monkey Island wiki
LeChuck's beard is a peculiar part of the evil demon-zombie-ghost pirate in his many incarnations. Most significantly, it is used to resurrect him in his zombie form, the first time he returned from the dead in a new undead form.
The ghost beard
At the end of The Secret of Monkey Island, Guybrush Threepwood destroys the Ghost Pirate LeChuck with a bottle of root beer from the Grog Machine. LeChuck blows up fantastically and the bird's-eye-view instant replay shows LeChuck's head flying high up in the air. Shortly afterward Guybrush collects LeChuck's beard, the only part of him to survive, as proof of the defeat, although this is not shown in this game.
In Monkey Island 2: LeChuck's Revenge, Guybrush shows the still-writhing ghost beard to Largo LaGrande, who steals it and plans to reanimate LeChuck's corpse. The Voodoo Lady confirms that this is possible, and Largo and the Voodoo Priest do indeed succeed in resurrecting LeChuck as a zombie.
The flaming beard
In The Curse of Monkey Island LeChuck is resurrected as a demon, complete with a flaming beard. In Escape from Monkey Island Murray claims that this is what melted through the mountain of ice LeChuck was buried under, prompting Guybrush to reply that "[he] knew [he] should have shaved him first."
The Zombie Pirate LeChuck's beard is presumably his human body's beard, years after his death and thus in a particularly gross state. It has no special properties or role.
In Tales of Monkey Island LeChuck returns to a human state, and his beard returns to the great size and lustre it presumably had in life.
ScrewAttack ranked LeChuck's beard first in their "Top Ten Beards List".