I'm trying to figure out what this process is called.

Example:
When I'm NOT logged into the site, and I want to click on the action on page 1, it will bring me to the login page. Once I'm logged in, it will forward me back to page 1.

How does it remember which state I was in? What is this process called, so I can search for google tutorials?

it is a cookie

oh yeah! that's right! thanks!

This could be that your state is saved into a session too.
http://www.php.net/manual/en/intro.session.php

Session support in PHP consists of a way to preserve certain data across subsequent accesses. This enables you to build more customized applications and increase the appeal of your web site.

Tripy, I hope you know, that session is based on cookies also (we are not talking about passing session ID through urls).

Tripy, I hope you know, that session is based on cookies also (we are not talking about passing session ID through urls).

Not necessarily, but of course I knew that.
I was saying session like "I have a variable set in my session" rather than cookie like "I have set a cookie valid up to 2100 with my login credentials in it"

:-D

It may also be in the url as a GET variable, I sometimes see in url:
site.com/login.php?id=...&next=...
the next variable (it can be in any other name ) saves the url where the user should be sent after log in.