wow!! the above explanations are very long and comprehensive, I would read them if I wanted to reeally understand how IPs function. But the cliffs note version is:
Every network is free to assign its own IPs. So when your router gets switched on and connects to your ISP, they give you the first available free address on the internet, within the boundaries they are allowed. They usually have a whole block they can use, like 124.125.x.x, where they can assign you any 2 values for x.
Also, when your PC connects to your router, there is a separate local network formed, and the router can assign any IP it wants to your PC, without affecting operations, any website you visit will still see a request from 124.125.x.x. So your router will give you any free IP address that any other PC on your local network hasnt already been assigned, for example, 192.168.0.3.
It’s almost as if every time you switched on your cell phone, you would get the first available number. Although, IPs can be set to be fixed, like telephone numbers, but if the settings conflict and two devices on the same network, like two PCs on the same laptop, are set by mistake to have the same IP, the network won’t function right.
OK never mind, my answer ended up being just as long :S