This is a variant of the English auction, most commonly used by fundraisers. Participants all write their bids on a sheet of paper. People can see the bids others have made, and can increase their bids accordingly. The auction finishes at a set time, and the bidder who has written the highest bid on the sheet wins the item.
It could be said that most online auction sites essentially hold silent auctions, in that there is generally no contact between the bidder and the auctioneer until the auction has ended. However, online auctions tend to last for days or even weeks or months, whereas real silent auctions usually end within a matter of hours.