From Unofficial BOINC Wiki
A numerical and unique identifier of a computer on the Internet. Addresses for version 4 of the IP Protocol are 32 bit values, represented as 4 individual blocks of numbers each with a value from 0 to 255.
IPv6 addresses are a little more complicated, and more info will be added here when their use is more widespread, IPv6 is still in the developmental stages and is not used by the masses.
Some of you are going to immediately ask, how can billions of computers be served by this absurdly low range of values. It is quite simple, we have in the Internet a network of networks. Each individual small network uses addresses within certain reserved address spaces for all of its internal identification, then this network uses a Gateway or Portal to connect the internal network to the external networks.