Private messages are those sent to the forum manager, normally through the link on the Discussion Home Page found toward the bottom that reads Post Message to Manager.  If anyone clicks that lilnk they will see an option to make a message private that isn't available when posting a standard message, either from the Discussion Home Page link at the top of the page or in reply to a message on the message board.

Now you can also toggle a button under Manage Forum/Toggle Forum Options that is called Private Messages.  This will open up the ability for all messages to be made private.  Normally this is set to false, and I recommend you do not allow everyone to send private messages willy-nilly, as it defeats the purpose of a public forum, which is the dissemination of information on the widest basis possible.  If you make private messaging available, you have essentially reduced your forum to just an email host, or an instant messaging service--not your goal I suspect.