Every single machine on the Internet has a unique address, {At least
one address, possibly two or even three---but we won't go into
that.} called its Internet number or IP Address. It's actually a
32-bit number, but is most commonly represented as four numbers
joined by periods (.), like 147.31.254.130. This is sometimes also
called a dotted quad; there are literally thousands of different
possible dotted quads. The ARPAnet (the mother to today's Internet)
originally only had the capacity to have up to 256 systems on it
because of the way each system was addressed. In the early eighties,
it became clear that things would fast outgrow such a small limit;
the 32-bit addressing method was born, freeing thousands of host
numbers.
Each piece of an Internet address (like 192) is called an "octet,"
representing one of four sets of eight bits. The first two or three
pieces (e.g. 192.55.239) represent the network that a system is on,
called its subnet. For example, all of the computers for Wesleyan
University are in the subnet 129.133. They can have numbers like
129.133.10.10, 129.133.230.19, up to 65 thousand possible
combinations (possible computers).
IP addresses and domain names aren't assigned arbitrarily---that
would lead to unbelievable confusion. An application must be filed
with the Network Information Center (NIC), either electronically (to
hostmaster@nic.ddn.mil) or via regular mail.