I do not know the etymology of these words or the history of their use in the context of air-fuel ratios, although their dictionary definitions (lean [adj.], rich, too bad I don't have an OED subscription) and usage in other contexts does parallel their usage here. I did some cursory research but gave up, the folks on the English site may be able to help there. However, answering your basic question:
The terms are relative in the same sense that "dim" and "bright" are relative:
- "Lean" means a lower fuel-to-air ratio; that is, less fuel in the mix; compared to something context-dependent.
- "Rich" means a higher fuel-to-air ratio; that is, more fuel in the mix; compared to something context-dependent.
If you say, "the air-fuel mixture is rich" (or "too rich", same thing), it is implied to mean that there is more fuel in the mix than there should be in whatever situation you are talking about.
Now, there's a commonly quoted stoichiometrically ideal ratio of 14.7 air:gasoline. "Stoichiometrically" meaning that 14.7 masses of air react with 1 mass of gasoline according to the chemical reaction equation. This is often the context. You can find an interesting discussion of the finer points of this number here, mostly centered on the definition of "air".
So in that sense, when speaking of gasoline, if you said the mixture was "rich" then it means the ratio is < 14.7:1 air:gas, and if you say it's lean, you mean the ratio is > 14.7:1 air:gas.
But 14.7 isn't the magic number for other types of fuels, and may not be the magic number even for gasoline depending on other conditions in the engine. If you're talking about those situations, "rich" still means more than whatever amount of fuel is ideal for the given amount of air, and "lean" means less.
I guess if it was neither "rich" nor "lean" you'd call it... just right?
Still, I do not know why "rich" and "lean" were the chosen words for this, and wouldn't mind finding out, myself.
Also just for clarity, this terminology doesn't apply to anything else in the vehicle does it?
I have never heard it used in any other context. The words "lean" and "rich" are so strongly associated with the air-fuel ratio that if you told a mechanic that the battery acid was "rich" I suspect they would either wonder why you had gasoline in your battery acid, or why you were trying to build an engine that burned battery acid as a fuel, heh.