Devices in a network have to be distinguished. Therefore addresses are assigned to the devices to identify them uniquely. These addresses are called IP (Internet Protocol) addresses. The IP was specified in RFC 791.
In general a IP address is just an enumeration. For the sake of structuring it is seperated into groups (or partitions, ranges). This grouping can be most easily seen in the so called dot-notation, that consists currently of four and in the future of sixteen numbers.
For daily use, one usually uses the name of a device or computer, its hostname.
Corporations lease one or more groups of addresses and can then use addresses of these ranges, statically or dynamically.
Beside public addresses, there are private address ranges, that are mostly used by smaller corporations and private users. There main difference is, that router do not route data streams between such private addresse in the public net.
See your IP adress.