After the post is promoted it should be shown in all subscription timelines/outlines in natural order by date.
For example, if user A is subscribed to user B and C. Then he sees posts from user B and C in his subscription timeline. When admin promotes a post from user X, then user A will see a single post from user X between other posts from users B and C.
Just like LeonidS said, and in more simple terms - it just pushes the post into feeds of people even if they don't follow the post author. Great tool for admins to promote great content and help members find who to follow.