https://portforward.com/
https://stackoverflow.com/questions/12290412/when-is-port-forwarding-necessary
https://superuser.com/questions/284051/what-is-port-forwarding-and-what-is-it-used-for

Most users don't need to explicitly configure port forwarding unless the software (game/etc) explicitly requires a particular configuration.

It's usually all controlled by the software firewall. The router options you're looking through are basically a hardware firewall.

If your network already works, and (hopefully) your firewall software already works, there's no need to configure these things in hardware. They provide finer control over network traffic/packet management and security, but they also introduce complexity. If you don't really understand what you're changing and what those changes do then you can basically limit or "lock out" normal networking functions, and depending on the specific options in your router hardware it can be fairly involved. Just use the default settings, whatever they are.

You can configure forwarding (and firewall, etc) directly through your router and, theoretically, remain just as "secure" without running firewall in software - and this would free up resources on the computer itself. But in practice it requires frequent maintenance and reconfiguration, every little update to every little thing can "break" settings which currently work, and it's a bit of an annoyance to go through the router config again and again each time you want to install some other new software (game/etc) or access new network things. I find it it's not worth the effort when decent firewall software (even Windows Firewall, which is surprisingly excellent) just handles everything well enough, quietly and automatically or with a one-time "yes/no" sort of user prompt.

I've never seen "famous server" and "famous game" before ... they're probably quirky translations of settings which "make server/game visible to the network".