Pop-ups are windows that open on their own, or as part of a web site, while you are logged on to the Internet.
Pop-ups can also acts as advertising on certain websites: sometimes legitimately, sometimes not.
Be aware, however, that some ad-supported programs (e.g. free online games) won't run if their ad components are removed. You'll either have to give them up, or, if available, pay the money for full no-ad versions.
Some spammers use Windows' built-in Messenger service, which sends messages in a broadcast across a network. The way to block these annoying messages is to disable the Messenger service. In Windows XP, you can do this through the Control Panel. Navigate to “Administrative Tools | Services”, double-click on “Messenger” and click on “Stop”. Then set the “Startup Type” to “Manual” or “Disable”. Click on “OK” and the pop-up spam should be blocked.