Recently re-watched SW- A new hope. The droid luke and owen (hey! the wilson brothers! coincidence? anyway…) purchase is deemed to have a “bad motivator unit”. bad what now? Is their such a thing as a Motivator Unit, and if so, what does it do? Or what does it do for droids? Man, i feel like i have a bad motivator unit sometimes…
Actually, I think the line was “That R2 unit has a bad motivator!”
Because an “R2 unit” having a bad “motivator unit” would just be silly. 
By the way, I’ve also heard it said that the R2 unit Owen tried to buy deliberately malfunctioned because it didn’t want R2-D2 to be separated from C-3PO. (I guess it knew they were friends.) But I don’t know where that claim comes from . . . the novelization, maybe? In any case, I don’t think it’s anything Lucas wrote.
As far as what a motivator does . . . I haven’t got a clue. Motivates them, I guess. 
And while I’m being nitpicky, the thread title should really be “A Long Time Ago…”
OK, I’ll stop now. 
Cafe Society is our forum for discussing arts and entertainment. I’ll move this for you.
DrMatrix - GQ Moderator
I remember a semi-serious discussion before Return of the Jedi was released to the effect that R2-D2 was the “Other Hope.” The “spontaneous” destruction of the other R2 unit was a strong clue that our R2 was strong in the Force…
The StarWars.com DataBank does throughly describes the purpose of restraining bolts, but is unfortunately silent on the topic of motivator units.
My thought is that perhaps the motivator unit somehow provides some sort of positive feedback to droids (something equivilent to pleasure) when they obey their masters. A droid with a bad motivator would be more like Bender than C3PO.
I seem to recall that it was an R5 unit (R2’s have domes, the R5 had a kind of trapezoidal head). I also seem to recall from some other source that R2 poured his mechanical little heart out to R5-D4 in the back of the Jawas’ sandcrawler, and R5 did indeed short out his motivator on purpose so R2 could continue his quest for General Kenobi. I suspect a droid with a bad motivator either has trouble convincing itself to do anything or just can’t move.
I’ve also wondered what that gear that fell out of either R3 or 3PO was (“Look, sir! Droids!”) and whether it was something important. Perhaps it was the part that let R2 remember that he had rockets built into him.
There was a short story from writer Peter David that cast the “busted” R5 as secretly Skippy the Jedi Droid.
Short summary: when Skippy was bought by Uncle Owen, it used its Jedi powers to forsee the future. Realizing that it was necessary for R2 to go with Luke and deliver Leia’s message, Skippy used the Force to self-destruct, setting destiny on the right track.
Assuming that the OP is looking for a semi-serious answer, I will try to provide one.
My guess is that Lucas was trying to use some of that there fancy science fictiony sounding language. In this case he appears to have done so more successfully than when he tried to insert “parsec” into the dialogue.
When the droid started to move, it went kablooie. That means that its “motivator”, that thing that provides “motive force”, no longer works. i.e., “this (unit) has a bad motivator” means “The thing that provides physical movement for this droid is broken.”
To be fair to Lucas, I’m not sure how else you could say the same thing succinctly as “engine” or “motor” doesn’t sound quite right. Perhaps “motivator” is the correct technical term in this case.
In the radio play of Star Wars, R2 sabotages the other droid so he would be able to continue his mission.
Which just reinforces the theory that R2 is, in fact, the most badass character in the SW universe.
The piece was part of C3P0’s massive droid wang, as glimpsed in some of the trading cards from the movie.
It was his foreskin, if you will.