1 And those a bit younger might be thinking of this: Bachman–Turner Overdrive

2 I've seen a few modern uses of it for being the highest gear in an automobile, but that's it.  Never made sense to me; why would it have a special name?  So it makes sense if it came from somewhere else having nothing to do with Messers. Bachman and Turner, either.

3 Gah!  Ninja'd by Siergen!

4 It did indeed refer to the highest gear in some cars, and the reason for the term is that when you're in overdrive the wheels turn faster than the engine.

It was thought up by a marketer, of course, and it was pushed because it seemed to imply "really fast". In a lot of cars with automatic transmissions, there was a special button on the console you had to push, or a special lever under the console you had to pull, to get into overdrive. I don't think there was any mechanical reason for that; it was just to make it seem special to the driver.

Like so many other "features" that didn't really make any difference except for advertising, the term eventually fell out of use.

5 An overdrive used to be a fully separate unit that was bolted to the rear of a transmission, the same way a transfer case is attached today on 4x4 vehicles with longitudinal architecture. For that reason it had a separate control, again the same as a T-case. It was possible to buy a transmission separately and attach an overdrive to it. People working on restomods do this even today. So, I don't think it ever was a marketing term, although it's possible, of course. I'm not versed in history that much. Over time, it became merged with the transmission as an overdrive gear (gearset - I think most or all of them were planetary), and then it was put under the control of the transmission itself. It became on the cusp of electronic control. At that point, the button morphed from a button that engaged the overdrive into a button that inhibited the overdrive, so that the transmission's control computer would not engage it. My jeep still has that on the 42RLE transmission.

In an odd twist of fate, the latest ZF 9-speed transmission, found in FCA and Honda products, has a whole of 4 overdrive gears. It's divided into 2 halves, linked with a dog clutch. Anything above that clutch is an overdrive. It is a fairly controversial design, to say the least.

6 I didn't know that. Interesting!

7 You mean, that button doesn't give the ship's AI "Maximum" control over all functions, so that it can go on a homicidal rampage? I'd assumed it was a reference to the movie.