Lots of games (especially console games) use p2p hosting/match making rather than central dedicated servers.
Manual port forwarding is annoying as different games use different ports and often you want multiple players behind one connection, most routers have UPNP or NAT-PMP to solve this where the game or app tells the router to dynamically forward ports.
Most of the Thomson's come with some kind of "symmetrical" NAT setup instead of full cone which doesn't seem to not work properly with UPNP / dynamic port fowarding.
The PS3 network and xbox live will list your connection as strict NAT if you don't have ports opened (dynamically or statically) for the game to act as a server in a p2p relationship,. Typically people strict NAT can't join other strict NAT games so it limits what games are available for you to join.
To get open NAT: You can muck around with telnet into the router consol to fix it (requires tech savy) or you can add static port forwarding (annoying) or you can replace the Thomson with something that doesn't have these issues (TP Link is good bang for buck).
If you search geekzone for either: thomson open nat OR thomson strict nat ..you will find lots of threads about this.