VoIP is an acronym for Voice Over Internet Protocol - also referred to as "Voice Over IP". In more technical terms, VoIP is the transmission of voice over packet-switched networks.
In more common terms, it means phone service over the internet. The quality is usually as good as or better than traditional phone service and much more advanced in terms of features due to the technology. Perhaps best of all is that it is less expensive than old-fashioned or "plain old telephone service".
Traditional telephone networks utilize citcuit-switching technology. This simply means that a pair of copper wires is used to connect one party to the other, completing an electrical "circuit". In order to complete the circuit for one phone conversation, two wires have to be physically connected (and only one conversation can be placed on that circuit at a time).
With packet-switching (IP based) networks, voice conversations are broken down into tiny "packets" of digitally sampled data. These packets are then sent over the internet to the called party. The receiving end reassembles the tiny packets of voice to make the audio understandable.
Using this packet-switching technology (VoIP) as many as 6,000 simultaneous voice conversations can take place on the same amount of copper wire that one voice conversation requres on the traditional telephone network.