Ok this should clear everything up. At home you have 2 kinds of IP addresses, your external and your internal. The external is that IP address that appears to the outside world (other people on the internet) this does not have to be static. Your internal IP address is the IP address that your router gives your computer and depending on the router, it may or may not be static. Routers will assign a specific address to a specific computer every time if static IP addresses are enabled. If not then Ip addresses will be given out to your computer for a given time period. If the computer does not communicate with the router within that time period, the next time the computer communicates with the router it will give the computer a new IP address. When port forwarding you can only forward a range of ports to a specific IP address so a static IP address is very helpful if your computer may be off for periods of time longer then the IP address lease time. So , in short a static IP address for your computer is the best idea, but not completely necessary.
