This screen shows you the messages you have waiting for you at the top, and allows you to send messages at the bottom. If you have a message, you can reply to it, or delete it by using options to the right of the message. To send a new message, simply select the Dominion you are sending the message to, type your message, and send.
It is also import to mention that you also have the ability to censor other dominion's messages. If you receive messages from a player and do not wish to, you also have the ability here to censor these messages.