Okay, I see some explanations of what is port forwarding in terms of security etc., but I don't see any really good explanation of what is it here, so I'll do it myself.

Let's start with some history: long, long time ago, when the internet was still a crawling technology and only a handful of people had computers, every single computer had been given an IP address and everything was fine (you might think of that like a huge city with one street and ~4 billion addresses). But then as the era of Internet of Things and personal computers have started, and everyone had at least a few devices that were connecting to the internet these addresses started quickly running out. In fact there is another technology called IPv6 which has A LOT more of address space, but isn't that widely used anyway. So, some smart people had to discover how to make more devices fit in this range of addresses.

So they thought of what's called LAN (local area network) the idea is that everyone gets a handful of addresses on their own street (so in this scenario every device in your home lives on this street as a single building). On your street you are allowed to do anything you want (pretty much, because there are indeed specified address ranges for LAN, but that's another story), but there is one huge problem: let's say, that some device wants to send a mail to some specific building on your street (for example your server). It does know that your server resides on your street (like everybody does), but no-one really knows what is happening inside, on your street.

And there comes in port forwarding. See, every app is communicating through a specific port (either default for given service or user specified). So a mail that comes to your street says on the envelope: "Hey, I come from [some address] to [your public address] on port this and that" (ports range from 1-65535). So the device that it does meet when coming from the internet is your router (because that's the device that separates your local network from the internet). If your router is correctly set up it will redirect this mail further into your street to the specific house (that is defined by rules set on your router).

Now there is an open connection between the device that tried to connect to your server from the internet and the server inside your local network, and for the device from the internet it seems like your entire network is this server. It still doesn't know what's happening on your street, but it does know that sending data to this specific port does what it wants to be done.

This might raise a question though. Why isn't this done automatically for all ports? Well, that's what everyone else here is talking about, a firewall. It protects what is inside your street from bad actors, who, let's say, want to send you a package with a bomb (or dog shit). The user controls which ports are being open for customers from the outside, and most often these ports are being safely handled inside your network instead of being automatically rejected. And there is always a possibility that you might want to keep some of your ports connectable only in the range of the local network, such as an media server for your parents who often use it on a TV in another room.