The Mark as Completed feature is used for marketing pieces that you may wish to post on social media, but do not intend to email to your contacts. Alternatively, they can be useful for creating a piece that you plan to re-use so you can easily copy it from the 'History' section.
Clicking Mark as Completed will send the marketing piece to the "History" section, and will preserve the marketing piece so your link[s] stay active on the various sites to which you may have shared the piece.