When you or someone else has a shaved pubic area.
During Rudy Giuliani's run as New York City's mayor he made efforts to clean up the downtown area. One day I heard someone refer to their privates as "downtown". I then named the act of shaving yourself "A Giuliani", because you "cleaned up downtown".
"Honey, you look like 1972 down there. I think it's time for a Giuliani."