It's sort of like email, except confined to this site. You can click on a member's name, which will take you to their profile, and one of the first options you'll see is to send them a Tree Mail. It is a private communication that only you and the member can see.
Or you can click on the little envelope at the top of the blue column on the left and select "Compose a new mail," but I find it easier to click on the member's name than to try to remember how to spell it correctly!
Hope this helps.
Edited to add: By the way, if that little envelope turns red, it means you have a Tree Mail.