Wikipedia: In computer networking, port forwarding or port mapping is an application of network address translation (NAT) that redirects a communication request from one address and port number combination to another while the packets are traversing a network gateway, such as a router or firewall. This technique is most commonly used to make services on a host residing on a protected or masqueraded (internal) network available to hosts on the opposite side of the gateway (external network), by remapping the destination IP address and port number of the communication to an internal host.
Port-Forwarding.net: Port forwarding, can be called port mapping. A word of definition of port forwarding is a way that bridge the communication between one side and another side. Normally, we surf internet by using a router. That means our computer behind the router. Our computer has a private ip address and the router has a public ip address. The requests of our computer will send to the router and the router will rely the requests to internet. This is how we surf internet. Router is like a front door before your computer. But if internet users or applications want to access your computer, it will reach the router(front door) firstly. If there is no port opened for this request in your router. Your router don't know how to deal with this, So your router will refuse the request directly. This will result internet users or applications cannot access your computer. Port forwarding is the right way to resolve this. What you need to do is just add a port forwarding entry into your router, then your router will know how to forward the request from internet users or applications to your computer that behind the router.
Webopedia: In home networking, port forwarding, also called port mapping or punch-through, enables you to create a permanent translation entry that maps a protocol port on your gateway machine to an IP address and protocol port on your private LAN. It's a transparent process, meaning network clients cannot see that port forwarding is being done. This process enables you to run a public Internet service on a machine that is otherwise hidden from the Internet by your gateway. Port forwarding may also be used to aggregate traffic from an application that uses several ports for transactions and consolidate it into one port for reporting the total traffic identified with that application.