In auction terms, the buyers premium refers to a percentage additional charge on the hammer price (winning bid at auction) of the lot that must be paid by the winning bidder. It is charged by the auctioneer to cover administrative expenses. The buyer's premium goes directly to the auction house and not to the seller.
For example, if you bid on a lot and win at £100 hammer price, and the auctioneer's buyers premium is 20% including VAT, you would pay £120 total to the auctioneer. It's recommended that you have your maximum bid amount planned out, so you can do the calculations of the additional fees prior to bidding.