Alf refers to Willie as Boxcar Willie because he used to ride trains by hopping into boxcars when he was young. Boxcar Willie was an American country western singer who adopted the moniker of the train hopping hobo after a character he wrote about in one of his ballads. His career spanned four decades, from the early 1960s until his death in 1999.
Willie discusses his previous dating adventures on the train with Alf, quoting the lyrics of Harry Chapin's song Taxi to describe the relationship.