The auction offers unique items that can't be purchased from the stores in the game. You can buy them immediately paying their "Buy now" price or try to win them by bidding.
If you are the player with the highest bid when the time runs out, the item will be yours!
If you are not you will take back 70% of the diamonds or 50% of the dollars you offered.
All items have starting price which is also the minimum bid you can place. To compete for the item you need to make an offer equal or higher than its starting price. When you make your suggestion you'll see if you are the highest bidder or not as the highest bidders and their offers are not visible to others.
If you place another bid for the same item you will pay only the difference between your current and your prevoius offer.