In simple terms, port forwarding or port mapping, is a common technique of forwarding a network port from one node to another. This method allows a public users to reach a certain port or service for a private IP address (usually in a LAN). For example, if you are behind a router, the PC has an IP of 192.168.0.2 while the router has 192.168.0.1. When you download with uTorrent, the requests are being sent by 192.168.0.1, but that IP belongs to the router, not the PC. Other users from where you want to download from will connect to router instead of your computer. A port forward (example port: 25678) will tell those external users that 192.168.0.1 is actually the computer. When opened on PC in uTorrent, port 25678 will permit communication between your computer and other users, therefore making you connectable.
To open a port, connect to the administration interface of your router, then go to Firewall > Forwarding rules or NAT > Forward/Port Forward (it differs from one router to another). In the Forward section, input the IP of your computer, then the port from uTorrent (you can find it in uTorrent > Options > Preferences > Connection) and check TCP and UDP and that's it. Eventually restart the router to apply the changes correctly.
