Afternic and Sedo publish a weekly report of domain name sales. Private sales don't appear on these reports. If you have your domain names listed at Afternic and Sedo there comes a time when you want to keep one of your domains and sales price private.
There may be a few reasons about this decision. You may want to buy a similar domain to the one you just sold that you think is offered very cheap compared to your sale. You could use the domain to substitute the domain you just sold in your portfolio or even offer it to your buyer for a quick flip. This similar domain might be coming up in an auction very soon so more attention will bring a higher auction price.
One other possibility is that you own many similar domains that you want to offer to the buyer once the buyer's identity is revealed after the sale. Many domainers are watching the Sedo and Afternic reports and a few are offering similar domains to the buyers. You don't want your email getting lost between 10s of emails from other domainers and hundreds of similar domains.
Also some domainers don't want to reveal what they buy and sell. They want to keep their strategy hidden. Especially if they want to keep their domain niche a secret.
Keeping your sales private at Afternic is simple and free. You just need to contact Afternic support and ask them to keep your sale private and that will keep the domain transaction from appearing on the weekly Afternic report.
At Sedo, apart from the usual 10%-20% commission, the seller (or buyer) may choose to further pay a publicity waiver fee of 2.5% of the sale price to request the non-release of the domain and sale price. This used to be free until Sedo got greedy and started charging this 2.5% fee. I don't understand why the fee is percentage based. Maybe I would understand a flat $15 fee but what is the point of the percentage? A 100k sale would incur a huge 2.5k fee. That is a lot of money for simply hiding a single sale. An average 15% fee should be sufficient for Sedo to offer clients such a simple service. Of course if the buyer wants to keep the sale private, he/she is the one to pay the 2.5% fee.
Actually the best way to keep your domain and sale price hidden is to use an escrow service like escrow.com or ecop.com. But that doesn't apply to sales coming through the Afternic and Sedo channels.