Verb:

Slang used in the furry fandom to describe masturbation, or the act thereof.

Originates from the slang term jerking off. Comes from that a furry's fursona most likely has "paws" instead of hands, thus the term for pawing.
(Usually used in the same context even if the animal has claws, hands, etc.)

Can be used in past (pawed), present (pawing), or future (paw) tenths.

Someone people turn to when they're sad who makes them feel better.

Making hands into a fist and rubbing them against another person in a cat-like manner. The act is usually done for attention or to annoy.