What is the difference between a background page and a popup page?
What is a content script?
Chrome extensions have many different terms that may look like similar. I will do my best to clarify those terms:
Background page: Basically a page that runs in background of the application, without displaying anything. The page will be granted every permissions you have requested in the manifest file. It should be used to access core-features as adding items to the context menu, read favorites, display a browser/page action.
Popup page: The name says it all, it creates a popup page. One particularity is that it will look like a "bubble" over the page. It can be quite helpful if a feature is not related to any specific url. Like the background page, the popup page will be granted every features requested.
Content script: A content script is basically a script that you can inject in the current page. Althought you cannot access custom variables directly, you may alterate the DOM and behavior of any page to add features into it. Note: you must request permissions on every domains on which a content script is injected.
To get you started, I would advise you to follow this tutorial:
Getting Started: Building a Chrome Extension
Almost anything you need to know about chrome extension development is already documented here. As a chrome extension developer, I find it really easy to use and up to date.