With PopupAgent running, the web-browser still requests a web page from the Web server - but before the request is sent to the server, PopupAgent intercepts the request and checks it to see if its a black listed site. If the request is OK then it is sent to the web server. The web server then retrieves the page and sends it back to the user's browser - but before the browser gets the page PopupAgent intercepts the incoming page. The page is then scoured for popups. If popups are found they are removed from the page - the page is then passed on to the user - popup free!
If the browser requests a black listed website or ad banner PopupAgent will stop the request before it is ever sent to the server. An "empty" page or ad is sent back to the user, thus saving bandwidth when blacklisted ad networks are requested, or blocking a site that is blocked by the black list.