Do you mean your IP in your LAN, or your IP on the internet? Most ISP's don't allow you to change your IP-address. They are sometimes dynamic and thus can change at any time.
When your PC is turned off the DHCP server (modem/router) will see the address is free and it will then assign the address to another device that enters the network. When you enter the network again, the DHCP server will assign you to the first available address.
It obviously is more complicated than I describe, buy that's how it can work.