An IP address is what identifies you on the internet. As IPV4 this identifier 4 digits (0 to 255) separated by a dot an defined to each devices connected to the Internet. This little number DYNAMIC TCP or be permanant but it is always unique, two devices can not have the same IP address unless they are connected in the same LAN or private. This is what happens when the connection is made from a box or ADSL router. In this case the router public ip address but apareils connected to gateways that are part of the same network that is local or private. Each device will have a different local address determined by the NAT (Network Address Translation).