You know I always love your explanations, Kirkus, and I know you know all about bias, but I think the analogy of idle speed on is somewhat misleading to those who are trying to understand.
If idle speed is set low or high, the performance of the engine under load can still be as good as would be otherwise. Whereas, the same cannot be said with a tube amplifier. Maybe the better analogy is idle mixture? But, even that somewhat misses the mark. We could also add timing into the equation, and that might be closer - but uh, but maybe we're getting more technical than we were allowed here...
Briefly, an underbiased amp will sound suboptimal, or even flat out poor, and there's not much that will change that. An overbiased amp will actually sound good; most often, even better than one biased to the manufacturer's spec.
Mark O'Brien of Rogue Audio once told me in his opinion, the biggest reason today's tube amplifiers sound better than those from the golden age may be bias. Amps back then were biased with the intent of maximizing tube life, as opposed to best possible sonics.
I have another friend who holds some out of fashion opinions regarding tube amps, and he biases his tubes to the point where the plates begin to glow, and then maybe (I said, maybe) backs off a hair. Now, he's converted his amp to use non-audiophile/guitar player desired output tubes, which he came into many lifetime's worth (and that's with the plates lighting up a bit) for simply the trouble of hauling them out of the place he got them. It's definitely the value play, as you're essentially dealing with "trash". As I've seen with my own fixed bias tube amplifiers, he'll adjust bias in front of you; higher bias is clearly superior, sonically. By superior, I mean, warmer, more liquid and musical sound overall, with better, tighter, more powerful bass, and yes, even improved imaging.
To take a stab at it in real, yet simple terms, it's the flow of electrons from one side of the tube to the other, which can be flat out or none at all. The optimal bias lies somewhere between those two endpoints. Given that optimal point is not going to be stable through the life of the tube and/or amplifier, you periodically adjust to maintain it.
For more of a silly explanation than that, so I can have someone kick me in the teeth, it could be likened to a pot of water on the stove. If the heat is off or too low, you're not going to be cooking, or perhaps at least, optimally. If it's too high, the water will boil over, and you'll wind up with a problem on your hands. You find the place where you get a nice boil without making a mess, that's where you bias your tubes.