It sounds like that was a PM (aka Private Message). They will pop up like that the first time you log in after you have received it. You can read and respond to it right there, or you can close it (as you did with the "x") and then go look at it whenever you want in your message folder. To get to that, look up in the right hand top corner of your screen.
The third row of text down (but still up in that corner), will say something like "1 New Message" Just click on that and your messenger screen will open. Then it's just like typing in a reply on the forum, but you are private messaging instead.
Once you start having more messages, then they will all be there, kind of like an "inbox" and you can manage them.