Every time you go online, on any sort of device, you will be assigned an IP address, or an Internet Protocol Address. This address provides information on what device you are operating, the internet service provider used and can even pinpoint where in the world you are sitting right now. And all this information is attached to every piece of data you send and receive via the web.
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.