Port forwarding from your router allows you to access your BlueSpray controller from any where on the internet.
Port forwarding is configured differently on different routers, but the idea is the same. Your router has a public IP address. BlueSpray controller (assumed to be on the network) has a private IP address. The router blocks all direct requests to all of the devices in its network by default, but you can configure it to bypass it.
The idea is to open a port on the router's public interface that forwards all requests to BlueSpray controller. BlueSpray has a web server that listens to 4 ports: 80, 8000 (http) and 443, 8443 (https). You don't want to use these ports on your router because you might need them to access your router. You should use different port, for example, router:8080 -> controller:80 or router:8443 -> controller:443. If your controller can only do port translation, you can use router:8000 to controller:8000 or router:8443 to controller:8443. Note that you can also change these 2 ports (8000 and 8443) in Settings->System.
Port forwarding will fail at times if your controller's IP address is dynamic. Since it it dynamic, it can change from time to time. When it changes, the router will forward to the wrong IP address. What you will need to do is reserve a fixed or static IP address for your controller. Different routers has different ways to reserve IP address. Please consult your router's User Manual for instructions on how to do it.
If you have any info about your particular router, please share it here.