A first-party cookie originates on the web site you are currently viewing (site customization, Login, etc.). A third-party cookie originates on a web site different from the one you are currently viewing (ads, shopping cart, etc.). Also, any unsecured content sent over http using SSL (https) is considered third-party.
Advertisers/marketers have found and invented so many ways to display ads that the answer is no (blocking 3rd party cookies will not stop all of the pop-ups you get). You'll need to use a pop-up blocker or a browser that has a pop-up blocking feature. In the case of IE, the new Google Toolbar has a pop-up blocking feature.