Auctions are used to sell many things in addition to antiques and art. All around the world there are auctions of commodities such as tobacco, fish, cattle, racehorses, and just about anything else where there's a market of multiple people interested in buying the same thing. That's the key to an auction - a bunch of people who are interested in buying the same object, and taking turns offering bids on the object. The right to buy that object will go to the highest bidder.
This is not the way many goods are bought and sold. If you go into the store to buy a soda, you're the only customer at the moment and there's a set price, a list price if you will. Shopping for a piece of jewelry? Chances are you're the only person interested in a given item in the jeweler's case, and while you may be able to bargain a bit, it's just you and the jeweler.
Now imagine you're at an auction and there's a great oak Mission-style rocker that you actually think was made by one of the masters. Somebody else in the audience thinks it's a pretty rocker that would look good in their living room, but they don't know anything about Mission furniture and its history. There's also a dealer in the crowd who knows the same thing about the chair that you do, and a collector of Mission furniture who's determined to add this rocker to her collection.
You are all willing buyers. There's only one chair. Who gets it? The highest bidder. What is the chair worth? Well that's up to you potential buyers to work out among yourselves, with the help of an auctioneer. You will determine the value, or "market value" of that rocker at this auction, in this part of the country at this time.
Now, I have an amateur's interest in real estate, and in that field you frequently run up against the term "fair market value. "Well, what is fair market value? The most common legal definition is that fair market value is the "price at which an item is exchanged between a willing seller and a willing buyer in an arms-length transaction when neither party is under duress to sell or to buy."
What better way to determine fair market value than an auction with an object offered by a willing seller and a bunch of willing buyers?