By default, Vanilla's recent discussions are ordered by most recent post (either discussion creation date, or most recent comment post date).
When you sink a discussion it won't be brought to the top of the discussion list when new comments are added.
You use this feature when you want a discussion to "go away" in a more subtle way than just closing it. We've found the feature to be extremely useful in the past.
Please note that sinking a discussion will not affect its' present order on recent discussions, it simply makes it so that new comments won't raise it again.