In the 2007 Michael Bay-directed movie they say it is short for "Autonomous Robotic Organism".
In 1984, in the G1 era, the faction name "Autobot" was never given a formal etymology. Consider, however, that all the "Autobots" in the original toyline transformed into either cars or trucks. This was a concious decision made by Hasbro, using previously issued Japanese (Diaclone and others) toy molds of various types. The decision, simply put, was: the cars/trucks/etc. were the good guys ("Autobots") and everything else (jets, guns, etc.) were the bad guys ("Decepticons). The second line of toys in 1985 saw the addition of non-automotive "Autobots" (ghetto blaster, microscope, dinosaurs, etc.) The faction name remained such until the Beast Wars era, when "Autobot" no longer properly described the new generation of good guys (now with animal altmodes), so it was changed to "Maximal".