When cats knead soft stuff for comfort.
Thought to be from when kittens kneaded their mothers tummy's to encourage milk flow.
Adult cats paddy paw anything soft and snuggly when in a cosy kitteny mood.
The cat may grip the item in its mouth while it paws or just paddy paw in a massaging motion going from left to right front paw.
Cats sometimes paddy paw their owners but as we don't have fur like mother cats it is somewhat painful. The hard core cat lady tends to endure this anyway.
Also known as baking biscuits.
My cat spends ages paddy pawing my fleece dressing gown whilst purring.