Your areola also has a purpose, and its tissue and fiber can help your nipples contract when you're cold, aroused, or breastfeeding.
Quite literally, puffy nipples occur when the glands or fatty tissue around a man's areola gathers together.
In fairness, the fact that men are attracted to all sorts of different body types — and — is an open secret among anyone who, well, knows more than a handful of men.