The internet is a lot of computers connected to the same network. In order to distinguish one computer from another, every computer is in theory assigned a unique number, also called an ip address. A typical ip address looks like this:
38.103.63.60 The above ip address is actually your ip address.
If you are behind a firewall or router, which is a device, through which many computers can connect to the internet, you may experience that more than one computer, show their ip address to be the same as other computers behind the firewall or router. This is because, it is actually the firewall or router, that is assigned the shown ip address. Behinde the firewall or router, the computers has unique ip addresses that isn't shown to any other computer than those behind that firewall or router.
So how does this site figure out, where in the world you are, just by looking at the ip address?
Well... actually it doesn't!
Every ip address is owned or assigned to somebody, and it is the address of the owner this site knows.
If you wanna know more about ip addresses, you can take a look at these pages:
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Howstuffworks •
Wikipedia