Port forwarding allows you to send traffic coming into your local IP address to a specific computer on your network. As you may already know, many routers are designed to block traffic from most ports for security reasons.
There are many reasons you may want to setup port forwarding on your router. Perhaps you want to run a game server, or maybe you want to host a website or database from your home. If you want to run a game server, there are private game servers that you can choose from. For instance, in Minecraft, one of the most popular games in the world, you and other players are free to build and explore anything you want in a 3D generated world. By running your own Minecraft server, you can determine the rules, and you and your friends can play together. If you, however, are of the opinion that you would need some basic idea and help on how you can set up a server for your game, you can look at online resources (such as the ones at https://www.linode.com/docs/guides/how-to-set-up-minecraft-server-on-ubuntu-or-debian/) and articles that can help you out.