A seller setting a price is guessing at one number: what somebody, somewhere, might pay.
An auction asks a room to reveal it.
The mechanism
Everybody watching has a private number — the most they would pay. Nobody says it. Bidding makes them act on it instead, one step at a time, and it ends when the second-highest number is exhausted.
So the winner pays roughly one step above what the second-most-interested person would have paid. Not their own maximum. That is the elegant part, and it is why a maximum bid does not mean paying your maximum.
Why this beats a fixed price
A fixed price is wrong in one of two directions almost always. Too high and it sits. Too low and somebody takes it instantly and the seller never learns what they lost.
The auction finds the number instead of guessing it. For anything where condition, rarity or taste varies — which is most of what sells here — that gap is large.
Where it fails
A thin room. Two people cannot discover a price; they can only split the difference between their own two numbers. This is the real argument for regularity — an audience is what makes the mechanism work at all.
Two stubborn people. Occasionally the price overshoots what anybody sensible would pay, because bidding against a specific person is a different motivation from wanting the thing.
An unclear item. A room that does not know what it is looking at prices the uncertainty, not the object. Which is the whole argument for describing the flaw.
What this means for a seller
Your job is not to set the price. It is to make sure the room has the information to find it, and to make sure there is a room.
More: setting a starting price.