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Theres different kinds of IP addreses - Internal IP and External IP. I'm going to use a hotel as an analogy. Inside the hotel are a lot of different room numbers, and each is a specific location. These numbers are used by the hotel itself to know what rooms there are -- this is like an internal IP address. Each computer inside your network is assigned a 'room number' that makes sense within your network. Each of these numbers (IP addresses) needs to be unique, since you can't have more than one 'room' with the same number.
Now, the hotel has a street address as well, and this address is used by the rest of the world to know where that hotel is. This is like your External IP address, which is assigned by your Internet Provider.
Probabally a daft explanation, but its the general idea :)