networking question

[Gerhard Magnus]

One thing I've always liked about computers is that it's possible for
one to do so much more than one understands; a little knowledge turns
out to have a great deal of leverage. But now I'd like to backtrack a
bit and learn something about the LAN I've already cobbled together.

My interface with the Internet is an Actiontec DSL modem (which I then
have connected to a router.) When I use a browser to look at the modem's
"status" window I see it's connected to a WAN (wide-area network?) which
I assume is administered by my ISP. The WAN information includes an "IP
address" and a "Gateway" which differ only in their last two sections
(i.e. IP address xxx.xxx.181.193 and Gateway xxx.xxx.180.1) Why are
these two addresses needed? (I'm thinking my LAN would only need one IP
address.)

Thanks for the help on what's probably a very elementary question....