What does it mean to say that my IP address is infected with a virus?

I got a message on my computer saying that it was infected. It gave a phone number to contact Microsoft. I called the number, which I assume was in fact Microsoft. If not, they went through a rather elaborate routine. The tech person I spoke to said that not only was my local computer infected, but also my IP address. They said that if I replaced my computer with a new one, the new one would be infected by the IP virus.

I just shelled out $500 to have them clean things up, including a firewall to secure my IP connection.

What I want to know is what it means to infect an IP address. Is there some server on the Internet that contains information? If so, what information?