The Vorpal Sword is the enemy of the Jabberwocky. At the beginning of the story, Alice is told she is supposed to slay the Jabberwocky with it. Sometime in the middle, the Hatter tells Alice the Vorpal Sword was stolen from the White Queen by the Knave of Hearts, Stayne. Later, the Hatter tells Alice that the Vorpal Sword is somewhere in the Red Queen's castle.
Alice finds the White Rabbit who apparently knows where it is and leads her to a small building being guarded by the Bandersnatch. Alice runs to find Mally and asks her if she still has the eye of the Bandersnatch. Of course, Mallymkun doesn't give in so easily, so Alice must steal it from her. She then gives the Bandersnatch its eye back and is able to retrieve the Vorpal Sword.
She runs to where the Hatter is being imprisoned and is about to cut him free, yet he tells her it can only be used to kill the Jabberwocky. Close to the end, when all escape, Alice uses the Vorpal Sword to defeat the Jabberwocky and save Underland.
The Vorpal sword is also mentioned in the poem "Jabberwocky".
One, two! One, two! and through and through
The vorpal blade went snicker-snack!
He left it dead, and with its head
He went galumphing back.