While advertising/sponsoring is a common way to publish and promote a product for free, some software advertising systems do more than just show static banners, they make secret use of your internet connection. For example, to retrieve new banner ads from a third parties' server or send various information about you. This information is collected and sold to third parties.
Because of the secret behavior of these systems, they are also called advertising trojans. Most of these systems are installed with a (often popular) host application, which may or may not work without the snoopware components installed. Some attach themselves to your browser, some are completely invisible.
To gain further information on adware/spyware and how to remove it from your system (for free) go to http://www.lavasoftusa.com/ and follow the links to download Ad-Aware.
For additional tips on recognizing and avoiding spyware, refer to this article from The United States Computer Emergency Readiness Team (US-CERT).