Zero-ping is when somebody plays on their own server. Thus, for them, there is no lag, and everything moves smooth as butta... Sniping the head off your opponent is as easy as taking down a bot, because you don't have to lead. The unfortunate OTHER player, on the other hand, has to deal with [typically abysmal on a 56k connection] packet loss, quarter-second latancy, choppiness, etc. It's a *huge* advantage for a zero-pinger.
However, if both people are LPB, or on a connected DSL or cable network, the zero-pinger advantage isn't that bad, even over 1000+ mile distances, if the network is good. I've played duels where my ping is a packetlossless 80ms, and they're playing on the server; with the exception of sniper weapons, it's pretty fair.