The Cheshire Cat is the cat of the Duchess. Alice meets it when she leaves the Duchess' s house, and sees it in a tree. It constantly grins and can disappear and reappear whenever it likes. Sometimes it disappears and leaves its grin behind. The Cheshire Cat is the only character in Wonderland who actually listens to Alice. He teaches Alice the 'rules' of Wonderland.
The cat sometimes raises philosophical points that annoy or baffle Alice. It does, however, appear to cheer her up when sentenced to death baffles everyone by having made its head appear without its body, sparking a massive argument between the executioner and the King and Queen of Hearts about whether something that does not have a body can indeed be beheaded.
When she grows and gets stuck in the house, the Rabbit orders Pat to get her out. In the end we discover that the White Rabbit is a herald in the Queen of Heart’s court. The White Rabbit is nervous and always in a hurry. However, he is confident enough about himself to contradict the King of Hearts.
