Hi,
That MessageID info is internal to Postmark. It is unique way to reference that message. For instance, if that message generates a bounce, the two of them will be connected by this MessageID. This information is guaranteed to be unique and is present in every message that Postmark sends.
Right now, by inserting Server ID and MessageID (Postmark MessageID) into URL you can navigate to web page showing all the info on that email (including full message body with headers). You can check this out by clicking on any message in your Outbound page. However, there is no API yet to support the same thing. It is in one of the immediate iterations, so it should be soon out, but I can't give exact ETA yet.
Regards,
Milan Gornik
Postmark developer, Wildbit