Where did you get the router? It is unusual to run a straight router to connect your LAN to the internet. You might run a bare router inside your LAN, if it's complex enough to need one (e.g., a fair-sized corporate office).
All the cheap home routers I'm aware of include firewall software. By default they block all incoming ports. To unblock a port, you have to configure the router to forward that port to one of the computers on your LAN. And if you do that, you'd better make sure the app that is listening on that port is free of security holes.
The computer has no firewall. The router seems to have a 100% effective firewall. When I run external programs that probe my system, they are unable to find anything.
I can see how that sentence could be confusing.