The term was coined in the famous rage comics on reddit.
Jim: Nah fuck that bitch
Tom: Do I really need that new TV? Welp, time to fap on it.
Tom: Fuck yes I need a new 60 inch plasma tv
When one faps on it, sexual tension is released through masturbation, resulting in a mind that is clear in thought and a rational decision can be made involving women, usually sexual decisions.
Bro 2: Fap on it. Then you'll know what to do.
A portmanteau of "fap" (slang term for masturbation) and the phrase "sleep on it" (think about something in the night and morning).
Jim: Fap-on-it man.
*an hour later*
Mike: Nah, I like blondes.