It usually means that you do not have any latency associated with communication for your program to run. Though, if you are running it off of your machine as a host, it would induce more lag on others who join into your machine, rather than having an actual server that has dedicated itself on managing traffic, and on top of that a regular household connectivity won't even be suitable for any type of decent hosting anyway.
Unless, of course, you are just going to run something simple like Ventrilo or TeamSpeak servers. In the past, when I was in the team, my teammate had setup a server at home for Ventrilo or TeamSpeak, and had our website running off of it.
No, even if you have a server in your room (which is separate from the terminal you are using) there should be something more than "-", unless the program that you are using is ignoring anything between 0~1 ping.
EDIT: Whenever I attended LAN events, I had 5ms minimum.