This term refers to depictions in early Hollywood movies where young boys would stand in place, holding large palm fronds, ceaselessly fanning Cleopatra or a Roman Emperor, etc.
The whole purpose of the fanboy's life was to support the pleasures and comforts of the object of their worship.
Hence, the slur, "fanboy".
Fan Boy: "Mr. Jobs, I so love my Mac. Am I fanning you to your fullest satisfaction?"
Steve Jobs: "iHarder. iFaster. Oh yes, Fan Boy! Don't stop!"