[exim] Is this mail relaying?

    I want to make a small LAN (about 4-8 computers) with a local mail server. Server is working, but it's behind a cable router so it doesn't have a public IP. I need to transfer mail, for example, to gmail and let it deliver where it supposed to. Is this what is called "mail relaying"? I'm very new to this subject, so, yes, I know I ask a stupid question, but I really don't know how to search for help if I don't know such a simple thing as "the name of my problem". BTW, is this posible? I was thinking of something like "if mail is from local host to non-local host then use gmail smtp". Thanx! :o)