What is an IP Address?

An IP address (Internet Protocol Address) is a 32-bit address used to identify your computer on the internet. This address is a string of four numbers separated by periods (such as 111.22.3.444). Each of these numbers is called an octet.

Each computer on the internet has a unique number in order for data to be sent to and from the computer. However, by using a router and NAT (network address translation) you can have one IP address and connect many computers to the internet. These many computers would share the one IP address of the router that is connected to the internet, so all computers behind the router would represent themselves as coming from the same IP address.

For more informaion on IP addresses, please take a look at these links:

Howthingswork.com - What is an IP address?
Arin - American Registry for Internet Numbers
Internic
Difference between static and dynamic IP address.
Difference between public and private IP addresses.