Are you seeing the message about having an unread message at the top of the page near the "logout" spot?
You probably have a private message that you can read by going to "my home", then to "my messages". The private message is like an internal email system for members and may be from anyone, whether you are playing them or not.
These are different than the ones you get from your opponent within the game you are playing that appear just above the chess board.
I hope that helps.