What does the Unicorn do in Through the Looking Glass?

Answer 1

The Unicorn is one of several characters in Through the Looking Glass who is based on a pre-existing nursery rhyme, in this case, The Lion and the Unicorn:

The Lion and the Unicorn were fighting for the crown:
The Lion beat the Unicorn all round the town.
Some gave them white bread, some gave them brown;
Some gave them plum-cake and drummed them out of town.

The action in Chapter 7, The Lion and The Unicorn reflects the action in the rhyme; When Alice first sees the Unicorn, he is fighting with the Lion:

Alice had no more breath for talking, so the trotted on in silence, till they came in sight of a great crowd, in the middle of which the Lion and Unicorn were fighting. They were in such a cloud of dust, that at first Alice could not make out which was which: but she soon managed to distinguish the Unicorn by his horn.

The fighting breaks off, and after everyone has some bread to eat, the Unicorn meets Alice, an encounter which spawns one of Lewis Carroll's famous Wonderland quotes, "If you believe in me, I'll believe in you"

`What -- is -- this?' he said at last.
`This is a child!' Haigha replied eagerly, coming in front of Alice to introduce her, and spreading out both his hands towards her in an Anglo-Saxon attitude. `We only found it to-day. It's as large as life, and twice as natural!'
`I always thought they were fabulous monsters!' said the Unicorn. `Is at alive?'
`It can talk,' said Haigha, solemnly.
The Unicorn looked dreamily at Alice, and said `Talk, child.'
Alice could not help her lips curing up into a smile as she began: `Do you know, I always thought Unicorns were fabulous monsters, too! I never saw one alive before!'
`Well, now that we have seen each other,' said the Unicorn, `if you'll believe in me, I'll believe in you. Is that a bargain?'

The Unicorn tells the Lion that Alice is a 'fabulous monster', which causes the Lion to address Alice as 'monster' for the rest of the chapter. He also demands a slice of plum cake, which he advises Alice on how to slice:

`You don't know how to manage Looking-glass cakes,' the Unicorn remarked. `Hand it round first, and cut it afterwards.'

The chapter ends with Alice being near deafened by the sound of drums, which causes the Lion and the Unicorn to leap up angrily, as it has interrupted their feast.

`If that doesn't "drum them out of town,"' she thought to herself, 'nothing ever will!'

Answer 2

In "Through the Looking Glass," the Unicorn is a character that Alice meets in the forest. The Unicorn is shown as proud and snobbish, boasting about its horn and debating with Alice about the existence of a moral compass. Ultimately, the Unicorn is one of the many fantastical creatures that Alice encounters during her journey.