A means of making telephone calls over the Internet.
Although principally thought of as the World Wide Web in the public mind, the Internet is actually just a communications system that can use a variety of protocols to transfer data, ie not just about web pages. It was being used for email and file transfer way before the World Wide Web became publicly available in August 1991.
Who cares? It works. How do you make it work for you is probably the better question. The basic needs are:
To be able to make free calls, the far end also needs to have similar equipment.
Calls to other VoIP users are generally free of call charges. With a facility like Skype Out, calls to overseas phones can be made at low cost since the sector to the country involved is via the Internet and from there it's a local call.
There's no 999 or 112 emergency service - you still need your landline or mobile for that.
If you use a firewall/router that's not equipped for VoIP, you may have to replace it (or update it) in order not to sound like you're coming from the bottom of a well. Whether or not this capital cost is worth it depends upon the volume and type of your calls.
Should you run out of bandwidth, the call can break up a bit, or sometimes drop you entirely. This is not good if you use it for business. Note that this is not a broadband versus dial-up modem argument, you may have more effective bandwidth available to you on a 56K modem than a 512K broadband connection just after schools close for the day. The solutions are either to get a dedicated broadband circuit for voice or make sure that your contention ratio is 20:1 rather than the usual domestic offering of 50:1.
Almost all of the major telecoms companies because they can squeeze more calls down their lines. Their big advantage is that they have complete control over the line and can therefore regulate the Quality of Service (QoS).
Interesting question: there are reported cases of people ditching their mobile in favour of a WiFi equipped PDA and using that instead of their mobile. The principal limitation is that you have to be within a WiFi 'hotspot' in order to be able to make calls. If you're not within range often enough, there are PDA/WiFi/phones coming onto the market which should allow you to select your communications method according to service availability.