2. papilla-a small nipple-shaped protuberance concerned with taste, touch, or smell; the papillae of the tongue. sense organ, sensory receptor, receptor-an organ having nerve endings (in the skin or viscera or eye or ear or nose or mouth) that respond to stimulation.apilla-a small nipple-shaped protuberance concerned with taste, touch, or smell; the papillae of the tongue. sense organ, sensory receptor, receptor-an organ having nerve endings (in the skin or viscera or eye or ear or nose or mouth) that respond to stimulation.