The IP in IP address stands for Internet Protocol. It is a technique used to computers in a network to communicate with each other. The most common application is the internet.
In an IP network, each computer is assigned an unique code (compare it with a phone number). This code is the IP address. Usually an IP address is associated with a company. In this way it's easy to figure out where alterations under an IP address come from. For consumers the IP address often corresponds with their internet provider.
IPv4 and IPv6
There are two types of IP-addresses, IPv4 addresses and IPv6 adresses. Since the supply of IPv4 addresses (e.g. 123.123.123.123) is getting scarce a new type of IP-address was created: the IPv6 adress. IPv6 addresses are the successors of the IPv4 addresses to make sure there are enough IP-addresses availbable for use. An IPv6 addres is different than an IPv4 adres since in the way that it has 8 groups of 4 characters (e.g. 2a01:7c8:aabb:cc::1). When you order a VPS with TransIP, by default you will receive a full IPv6 range.