Located at the bottom part of your screen, the Mailbox is divided into three sections: Ordinary Mail, Battle Report, and Alliance. Ordinary Mail is where you will get updates about Rewards, Resource Collection, and Game Notices. Battle Report gives information on PVE/PVP battle outcomes and Raid results. Alliance Mail contains notices regarding new Alliance Members and changes to your Alliance War Status.
Visit Kingdom Hunter's Official Guide for more information about the game.