If a man is paunchy, he has a round, fat stomach. The paunch is the belly; paunchy is how we describe the person who has it. It is informal and a bit teasing, with the same social feeling as paunch — often used about men who have grown a beer belly with age or sitting still. We do not normally use it about women or children. Though actually, English is not perfectly tidy: some people also say a paunchy belly, putting the adjective on the stomach itself. The kind thing to hold onto is still the pair: he has a paunch / he is paunchy.