Every computer connected to the internet has a unique public address known as an IP address. The current IP address space (IPv4) consists of 4,294,967,298 addresses. Of these addresses some are reserved for private networks (about 18 million) and others for multicast (about 270 million), so in theory there can never be more than 4 billion computers and servers connected to the internet at any given moment. This is a limiting factor since there are about 7 billion people on earth. There is a new addressing schema being implemented (IPv6) that has 340,282,366,920,938,463,463,374,607,431,768,211,456 possible addresses.
Some providers want to discourage their clients from running a server (mail, ftp, game or other) on their computer and therefore change the public IP address the user gets regularly. Other providers have fewer addresses than they have subscribers and therefore assign a random address to each user when he connects to the internet and assign that same address to another user after he disconnects. Both these processes are usually done by the Dynamic Host Configuration Protocol server (DHCP server).
Some people want to run a mail, ftp or game server on their computer and for that software to run it is usually necessary to enter the public IP address currently assigned to the user into the configuration. Other people would like to use a remote desktop application and want to know what IP address to connect to from a remote location.
The currently used IP addresses (IPv4) look like four blocks of digits ranging from 0 to 255 separated by a period like "192.168.0.255".In the new schema (IPv6) addresses can be written in different ways: