Port Forwarding
The big difference between this and port triggering is that forwarding is fixed.. you forward a port and it is always forwarded.. IE available to connection.. basically the forwarded port is excluded from the fire walling abilities of the router. Second it is static and applies to one machine only. Whereas you could set port triggering to the router and thereafter any machine on the LAN can trigger it unless its already in use.. port forwarding must be specified for each individual machine.
Port forwarding requires you to give each PC on the network its own unique static IP address.. Although there is ssh port forwarding that can be set dynamically. Most users only have the option of static ip port forwarding.
The real downside of port forwarding is that it can be very tricky to set up... You may have to allow a series of ports on a machine and have to do that for each machine you want to allow through. Also routers often have limited abilities and may not allow you the ability to forward a port or select the service you require.
Port Triggering
This is a way of Dynamically assigning a service to a port WHEN it is required by an outgoing service. The port is initially not allowed so nothing can get in and you are protected by your network.
A good example of this is when using Yahoo! voice .. the voice works fine for a few minutes after you connect to Yahoo! then Yahoo! sends some kind of packet that requires a response from your PC... The packet is allowed in through your router no prob but the outgoing reply is not authorized to open a port on the router and is thus blocked.
'ope this helps 
