Jean, here's what I found about private auctions on eBay:
"Private Auctions:
Strictly hush, hush — use this auction to protect a buyer's privacy. Bidders' email addresses won't show up on the item or bidding-history screens.
When the auction is over, only the seller will know who bought the item. This option can't be used with Dutch Auctions."
I only found about six Private Auctions currently going on eBay and some of them were for racy stuff like fancy underware. At least one, though, is for a big-ticket item. I suppose some buyers don't like the spam that can come from bidding openly on eBay. And I guess any bidder can join in on the fun; his or her identity won't show on the bidding record or as high/winning bidder, that's all. I think sellers have to pay extra to make their auction private.