This is an auction where the final bid for an item can be rejected by the seller if it is not high enough to satisfy them. They may set a particular fixed reserve, or they may alter the reserve over the course of the auction in response to the bids placed. Bidders are often unaware of the reserve price.
No reserve auction/absolute auction
This is an auction where the seller sets no reserve price. This is usually done in the hope of attracting large numbers of bidders hoping for a bargain. If this works, the item may end up selling for a higher price than if it had had a reserve.