In a typical home network arrangement (fig 1) various devices e.g PC, Laptops, Mobile Phones etc can be connected to a router to access Internet or outside world. As you can see in the below figure router has an external IP address assigned by which devices communicates with outside world. Each devices also have a private IP address assigned by which they can communicate with each other.
Now think of a scenario where you want to access your Home PC via RDC( Remote Desktop Connection ) from your office laptop. Without doing any special arrangement you reach upto your router IP address but can't reach to your PC becasue it lies beding the router and is hidden from outside world. Here actually port forwarding comes into picture which allows a specific outside world request to be redirected to any of the devices connected with the router. In our example RDC port 3389 can be forwarded to PC's local IP address and thus it can be accessed from outside world.
Although concept remains same but router specific settings may vary from manufacturer to manufacturer. Here are some standard rouuters and their configuration :