Since Vanilla's Recent Discussions are ordered by most recent posts (either discussion creation date, or most recent comment post date), there is sometimes a need to remove popular discussions and topics from their position on the list, while not closing or deleting them. This may come from the post being popular but off topic or no longer being relevant.
Who Can Sink Discussions?
The ability to Sink discussions is a permission that should be restricted to a select few users like Administrators and sometimes Moderators.
To sink a discussion you can click on the Cogwheel on on the appropriate discussion and select Sink:
To “Unsink” a discussion you again have to click on the cog wheel and then click “Unsink”
This permission is controlled by Roles and Permissions. A user would require the Sink permission under Default Category Permissions or the Sink permission for that particular category.
Please note that sinking a discussion will not affect its present order on the Recent Discussions page, it simply makes it so that new comments won't raise it to the top again.