The Monster has a long body with a snake-like head, multiple snakes for hands, and a spider on his head used for his "hair" (as said in the opening song This is Halloween).
The Monster seems to be kind of friendly, nice and happy-go-lucky.
The Stairs Monster (or the "one hiding under the stairs") is first seen saying the line "I am the one hiding under your stairs, fingers like snakes and spiders in my hair" where he emerges from the stairs. He and the residents of Halloween Town are later seen celebrating Halloween where he and the other citizens welcome Jack Skellington during the opening song "This is Halloween". The Monster is later seen with the other citizens during the Town Meeting where Jack tells the citizens about Christmas where he and the other citizens like Jack's performance. Later when Jack plans to take over Christmas, the Monster and the other citizens are seen preparing Christmas supplies for Jack, which only results in a disaster (as said by the Mayor who found out that the Christmas plan was a bad idea). Later during the end of the film, the Stairs Monster and the other citizens of Halloween Town discover that Jack is alive after he saves Santa from Oogie Boogie and helps him undo Jack's wrongdoings in order of what he did in order to save Christmas as he and the other citizens celebrate Jack's return.