Send system message to user
Try the notifications framework:


  This is a complete Subscriptions/Notifications Framework aiming at extendability and scalability. It allows any number of plug-ins defining new event types or subscription types or a different user interface.


Its a full featured module with a number of companion modules for sending messages via different channels depending on different events but what you're probably looking for is the 'Web messaging' submodule:


  Sending Method: Show messages on user's page