The post assumes that you have a basic knowledge in Chrome extension development, if not check it out here http://code.google.com/chrome/extensions/getstarted.html
In the manifest json file, there might be two properties definitions for background-page and content-script. These properties are the most common used in the manifest file of Chrome extensions. They are also the most important entities to understand the architecture model of Chrome extension. Remind a bit about Chrome browser, in Chrome we can open many tabs as we want, but the extension is always stayed on top of those. The extension is like a small program sitting on top of the tabs and no matter how many tabs we open, there is only one instance of extension running and executing.
The architecture model of Chrome extension
Now back to the background page and content script. The background can access to mostly many properties of the browser such as history, bookmark ..etc… but cannot access the user page nor the content script. However, the background page can make a call to execute the methods inside the content script and if the content script want to access the data in the background page, it has to make the request to the background page via method
chrome.extension.sendRequest. The background page on the other hand can make any cross site requests but the content script cannot due to the security of cross site scripting. The only options for content script is to make the request with JSONP to a service or make the request to the background page to make the request to the required service.
To summarise things, if your extension is communicating with a certain Web services or APIs. That has to be done in the background page. If the extension wants to modify the view of user page, it must send request or execute the method defined in content script then the content script will access the DOM elements and modify the view accordingly. If the extension wishes to receive some data from the user page, then it has to be done in the content script and the content script will send the data to background page via the Chrome extension request. Finally note that the background has only one instances over many tabs or page, but the content script is created new on new page reloaded or open.