"IPV4" is a basic system used in computer networking; the Internet builds on IPV4 as a foundation.
Every device connected to the Internet needs to have an "address"; IPV4 allows for a certain number of addresses. With the explosion of networked devices, like computers, smart phones, and even networked scales (!), we are running out of addresses. Recently the last block of unassigned addresses was given out to Internet Service Providers (ISPs); in theory that would mean we couldn't add any more devices to the Internet. To allow more devices on the internet, a new protocol named IPV6 was designed, which adds a lot more addresses, but is only partially compatible with IPV4. Eventually Internet connected devices will be IPV6-compatible, but there are a lot of things that ISPs can do to delay and ease the changeover. It will be many years before most people are affected. So there is no need to be concerned right now!

If you are buying network equipment, like a router or a DSL- or cable-gateway, make sure it says it is "IPV6 compatible"; if it doesn't say that on the box, it is probably not able to use IPV6 addresses. Making sure anything you buy now is IPV6 compatible will prevent you from being forced to buy a new one when the transition to IPV6 is completed.