Port forwarding allows for a direct connection from one client to another. Effectively when a VPN let's you port forward if you go to the external IP address they assign + the port they assigned they will be able to directly connect to a port that a program/service is listening on.

Torrent sites are only telling your client who to connect to via the tracker, your client still needs to be able to connect to them. You can still download without this but it is generally slower (may be going through a relay) and you cannot seed torrents except for anyone that can directly connect to you on whatever VPN you are on.

*Likely some mistakes above. Keep me honest denizens of the web.

I feel like its kinda late to learn now lol. Jokes aside, but its hard to find a good vpn with port forwarding nowdays, I dont know is there any at all. Im not expert, but forwarding will help a lot with seeding and thats the point of torrenting

Edit: you can still use torrents without port forwarding, it wont mess up your download speed

It forwarding opens a port direct to your system from the vpn ip.

So if your internet address at your router to your ISP is 1.1.1.1(which NATs it to your PC address on your lan) and the vpn exit address is say 10.10.10.10

Then when you port forward a port, say 443 (you wouldnt) then any request to 10.10.10:443 would then go to 1.1.1.1:443 and then to your pc on your lan.

In short it allows a direct connection through the vpn

Edit

Technically that's slightly incorrect,

packet goes on 10.10.10.10:443 but it goes to the PC directly through the vpn tunnel. The port it goes through the 1.1.1.1 router to the PC on could be anything, it won't necessarily be 443. It will be whatever the vpn is set to use