When you use port triggering on your router a connection attempt must be made from your computer to an address on the trigger port. When you router detects the connection attempt your router then turns on the ports, thus you have port triggering, a on/off switch for port forwarding.
Well the problem comes if you are using port trigging for a program that doesn't make a connection attempt, such as say a ftp server or hosting a game. If a connection is never detected the router never enables the ports.
Well that's what Port Triggering Initiator is designed for. You enter the triggering port to make a connection on and give it a address outside your network. Any address will do even if the connection fails its the attempt that triggers the ports.