wordpress migration database

I’m moving a wordpress site from it’s hosted location to my local LAMP stack. I’ve looked at the wp-codex directions for “If you want your old blog to work.” My question belies my little understanding of what is actually happening under the hood in wordpress, but here goes:

I’m downloading the site files and database twice, once the original, once with the new URL filled in the Settings. Then uploading the site and database to the new server(or to the local server in my case). My question is this: in order to preserve the old site(hosted) why can’t I just go back to Settings and reset the URL? … maybe I just answered my own question…

Anyhow, I’m asking because I’m still trying to understand how wordpress works specifically how it interacts with the database. It’s still a bit of a black box to me.

thanks