Any developer can "disable" one of their add-ons by going to the Edit Add-on page and clicking the Disable button at the bottom. This will cause the add-on to become inactive and not show up in any search results, display pages, or automatic updates.
It can be re-enabled at any time from the Edit Add-on page.
Admins can disable an add-on by changing the add-on's status to DISABLED from the Add-on Manager. Add-ons that are disabled this way will show up in the developer's control panel, but not be editable in any way.