Fonz is pronounced “fawns,” so the joke is that he heard “would you like some headphones?” And he corrected her pronunciation, meaning he interpreted it as “would you like some head, fonz?”

> I have no idea who the fonz is

Someone already answered the rhyming part, but since you don't know the show...

Happy Days was the name of the show and started in 1974 and went on for 11 years/seasons. It was kind of "the 1950's / early 1960's show", depicting a rose-colored view of the 1950's high school scene. Probably connected to George Lucas' 1973 film American Graffiti in spirit, which depicted early 1960's "hanging out" lifestyle - and also had Ron Howard as an actor in it. You could probably throw in Grease the theater play in 1971 as an inspiration/trend of this 1970's glorification of 1950's culture.

Fonz was always doing the stereotype of cool and had plenty of girls while the mainstream kids in the story went to him for advice and lessons about things parents and school don't teach you.