Charming Customs of the Olde Worlde

Guy: This is a traditional ceramic object, when a boy wants to marry a girl he give her this bird. Word for this bird is the same as, how do you call it in English? (points to crotch)
Me: Uh... cock?
Guy: Yes, in those times, boyfriend cannot show girlfriend his cock. So he give her this and say, I give you my cock. He say, mine is even bigger than this. Now, it is different. Now, boyfriend show girlfriend his cock right away.