To be more specific, these are message tracking logs. It's safe to delete or move them to a different location. Before you do that you could use the message tracking center to find out why there's such a high volume of messages flowing through your server.
I can see the messages in message tracker, but how do I view the headers? I think something is using the server for spam but I've run TDSS Killer, Malwarebytes and Hitman Pro but only TDSS identifies a suspect service which I'm reluctant to delete as it's the same as a valid service for licensing.