Mail in GoW consists of 4 types arranged in columns. There are many notifications so at times it will be hard to keep deleting it. Over time it will delete itself, but be aware there may be hundreds of messages by then. At this time you may only delete 20 messages at a time. You may also compose mail to people from here, or by clicking on their city, occupied tile and/or hero.
The inbox is where you will see messages from other players, as well as Athena and sometimes the Casino. These are generally notifications if from the later of the two.
This is where most of your mail goes. Battle reports, gathering reports, rewards, prizes are all filtered here.
It's where you save messages you star.
This is notices about members of alliances joining/leaving.