Voice over IP is the ability to make regular phone calls over the Internet. You will see it referenced frequently by the letters VoIP.
With VoIP your phone is connected to a box that connects to the network or you have a special phone that plugs in your network. Either way the phone still looks normal with a handset and a keypad on it to punch in your phone numbers. You will have a regular phone number and people using regular phone service (sometimes called POTS or Plain Old Telephone Service) can still call you as they had and you will still call them like you normally did.
The difference is you are now using an Internet service that transfers your calls to the regular telephone network. For the consumer the service most regularly recognized is Vonnage. You can also get VoIP thru many of your Internet Service Providers and they will often bundle the phone, Internet and TV in a package.
At large organizations they may set up their own VoIP system and connect to the telephone company. Cisco is a provider often of the software and hardware and phones for these systems.
With VoIP you probably will only get voice service and ability to transfer/forward calls, but in some cases you can also get video with the calls where people can send the person they are talking with.
The disadvantage of VoIP is that when your network or Internet connection is down you have no phone service.
VoIP is getting installed more and more in the world. The user usually notices no difference in quality of the calls (if any noticed it is usually an improvement).