Did they ever explain it?

http://www.sitcomsonline.com/photopost/data/745/WK017.jpg

It came from his pretending to play the bass: "Boom boom boom boom."

Kotter: What do you want to write your essay about?
Freddy ‘Boom Boom’ Washington: (Acts out playing a Bass Guitar)
Kotter: Oh, you want to write about playing Bass?
Freddy: Na man, I want to write about PRETENDING to play the Bass.

which as i recall, he only did that once on the show.

That's cool! I always wondered how he got that nickname!