the Cheshire Cat is the cat of the Duchess. Alice first meets it in chapter 6 from “Alice’s Adventures in Wonderland”, when she leaves the Duchess house, and finds it in a tree. It constantly grins and can disappear and reappear whenever it likes. Sometimes it disappears and leaves its grin behind. In chapter 8 she meets it again in the Queen’s croquet garden.
In “The Nursery ‘Alice'”, Alice notices that the cat has ‘lovely green eyes’.
The Cheshire Cat is the only character in Wonderland who actually listens to Alice. With his remarks, he teaches Alice the ‘rules’ of Wonderland. He gives her insight in how things work down there.
It is not 100% clear why Carroll named this character ‘Cheshire Cat’. “To grin like a Cheshire Cat” was a common phrase in Carroll’s day. Its origin is unknown, but it may have originated from a sign painter in Cheshire, who painted grinning lions on the sign-boards of inns in the area.