It seems likely that no one really believed that they actually did. There's no convincing explanation of why Cheshire cats were imagined to grin. Pendennis in his droll, humorous way, 'That woman grins like a Cheshire William Makepeace Thackeray also used the description well before Dodgson, in The Newcomes memoirs of a most respectable family, 1854–55: John Wolcot, the poet and satirist, who wrote under the pseudonym of Peter Pindar, included it in his Works, published variously between 17 - 'Lo! like a Cheshire cat our court will grin'. We do know that Lewis Carroll (The Reverend Charles Lutwidge Dodgson) didn't coin the phrase himself, as there are citations of it that pre-date his stories. 'They all can,' said the Duchess 'and most of 'em do.' 'I didn't know that Cheshire cats always grinned in fact, I didn't know that cats COULD grin.' Quite jumped but she saw in another moment that it was addressed to the baby, and not to her, so she took courage, and went on again: She said the last word with such sudden violence that Alice 'It's a Cheshire cat,' said the Duchess, 'and that's why. Speak first, 'why your cat grins like that?'

She was not quite sure whether it was good manners for her to 'Please would you tell me,' said Alice, a little timidly, for Of course, we know the phrase because of Lewis Carroll's Alice's Adventures in Wonderland, (published 1865) and John Tenniel's illustrations in it:

What's the origin of the phrase 'Grinning like a Cheshire cat'? Animals What's the meaning of the phrase 'Grinning like a Cheshire cat'?.

Grinning like a chessy cat