It’s an auction conducted at the airport terminal. In this auction you are a seller and you are bidding to sell your ticket back to the airline.
Optimists look at this and contemplate the efficiency gains: this is a mechanism for appropriately allocating scarce space on the plane. Pessimists detect a nasty incentive: now that the lowest bidder can be bought off the plane the airline has a stronger incentive to overbook.
The pessimists are right precisely because the optimists are right too.
Consider standard airline pricing with no overbooking. You buy a ticket in advance for a flight next month. Lots of uncertain details are resolved between now and then which determine your actual willingness to pay to fly on the departure date. One month in advance you can only form an expectation of this and that expected value is your willingness to pay for a seat in advance.
This is inefficient. Because, after the realization of uncertainty it could be that your value for flying is lower than somebody else who didn’t buy a ticket. Efficiency dictates that you should sell your ticket to him on the day of the flight.
One way to implement this is to hold an auction on the day of departure. Put aside the issue that flyers want advance booking for planning reasons. Even without that incentive, just-in-time auctions solve the inefficiency problem with conventional pricing but airlines would never use them.
The reason is that an auction leaves bidders with consumer surplus (or in the parlance of information economics, information rents.) As a simple example, suppose there is a single seat avaiable on the flight and two bidders are bidding for it. An optimal auction is (revenue-equivalent to) a second-price auction so that the winning bidder’s price is equal to the willingness to pay of the second-highest bidder. That is lower than the winner’s willingness to pay and the difference is his consumer’s surplus.
The airline would like to achieve the efficient allocation without leaving you this consumer’s surplus. That is impossible in a spot-auction because the airline can never know exactly how much you are willing to pay and charge you that.