IP Addresses are like mailbox numbers on a street. When the mailman wants to deliver a message to you, he needs your house number and street name. The same thing goes for IP Addresses - they logically define where you are, or in this case where your computer is.
Don't take that statement the wrong way - IP Addresses don't give away your geographical location. They just give a computer network a way to access where on that network you are. Sometimes, certain IP addresses are only given out in a specific geographical region, leading to a myth that once the cops have your IP address they are going to be banging down your door.
In networking, two basic addressing schemes exist - IP and MAC. A MAC address is like a person's Social Security Number. From the time you're born until the time you die, you always have that same social security number with you. But your street address (IP address) can change over time.
The MAC address of your computer is embedded in your Network Interface Card...basically, where you plug in the wire so that you can connect to the internet. This MAC address is unique to the card and will only change if you buy a new one.
The IP address of your computer is usually assigned by the network you connect to, and can change at any time. If you move your computer to a different network, odds are you're going to have a different IP address.
Now, there is MUCH more to IP addresses than that. I've just tried to provide a brief overview of what the address means and how it is assigned. If you like, I would suggest purchasing an introduction book to networking. It'll help explain things much more. Another option would be to try and find a Cisco Networking class. I'm fairly certain anyone can sign up. Check it out at www.cisco.com