In a traditional auction a seller offers a very specific and unique item for sale, and the buyers bid on the item. The highest price always wins the auction. In reverse auctions several sellers offer their items/service to a single buyer. The buyer creates an auction where he described his intent to purchase a relatively precise service or good. Each seller will then place their bid (offer), and compete against each other on prices but also on more immaterial aspects such as their location, reputation, etc... The buyer will compare each bids and select which one seems best fitted to his needs. In reverse auction the buyer will compare more than the price alone.
To resume, Reverse auctions save money to the buyer and help seller to only pitch their service to qualified customers. Regular auctions maximize seller profit while buyer purchase at the highest price and can only be seen as winner in non-monetary terms.