An auction in which the bids are submitted in writing.
The primary benefit of this is that you don't need to have everybody present all at once -- you don't even need an auctioneer present. There is some sort of sheet, and people write their name (or other identifying label) and their bid on it when they get the chance. Silent auctions may last for days.
Silent auctions can also be done anonymously; people are given numbers instead of names. This works particularly well on-line.
Usually the previous bids are visible, but occasionally the auction will be run like a ballot box, where no-one is aware of how much the others have bid.
These are often held as part of a fundraiser.