If you’re doing a peer-to-peer (P2P) related activity, port forwarding is very important for improving speed or enabling the service at all. That’s because your router blocks incoming traffic from certain ports by default, ports that are used for a P2P connection. To get around this, you can ‘forward’ the specific port that is used for the P2P activity you’re using, letting your router know that the traffic you expect to see from a specific port is good to let through.
You can simply leave port forwarding to your personal router, but if you want to stay anonymous while participating in P2P connections, then you’ll want to use a VPN service. If a VPN service doesn’t utilize port forwarding, then any P2P connections you use will either be straight up impossible, or very slow over the VPN. The P2P service you’re attempting to use needs to access a specific port on the VPN’s router, which needs forwarding to work properly. For example, you wanted to host a gaming server without giving away your actual IP address, then a VPN with port forwarding is desirable. The same can be said for torrenting.
TL;DR: VPNS with port forwarding matter if you want to stay anonymous while using P2P services.
Specifically, it’s any peer-to-peer (P2P) connections that utilize a port that’s not open by default on your router. P2P connections that need forwarding are used in services like PC gaming (usually in older titles or some indie games), VoIP, torrenting, etc.