VoIP stands for Voice over Internet Protocol.
As the term says VoIP is the transmission of voice communication through IP packets and, therefore, through the Internet. VoIP can use accelerating hardware to achieve this purpose and can also be used in a PC environment.
Webopedia defines it as: A category of hardware and software that enables people to use the Internet as the transmission medium for telephone calls. For users who have free, or fixed-price Internet access, Internet telephony software essentially provides free telephone calls anywhere in the world. To date, however, Internet telephony does not offer the same quality of telephone service as direct telephone connections.
There are many Internet telephony applications available. Some, like CoolTalk and NetMeeting, come bundled with popular Web browsers. Others are stand-alone products. Internet telephony products are sometimes called IP telephony, Voice over the Internet (VOI) or Voice over IP (VOIP) products.
If you are wondering whether this is something that can just replace your standard home telephone service, the answer is that many are doing just that, and Vonage seems to be the popular choice. See the Vonage section of this FAQ, and check out users comments about the service in the forum