I will try to explain in layman terms. The concept of port forwarding comes into picture when a host in WAN side( eg. Internet) need to contact the Private Server/PC hosted at the LAN side of a modem.
Having an IPv4 Public address for all the clients in the world is not possible due to technical limitations, but this problem can be solved with Port Forwarding.
Use Case #1
let us Say you have a static public IP address (184.108.40.206)for your Modem from the ISP.You also have a linux PC connected to the modem with private IP 192.168.1.15.
In this particular condition the PC host cannot be reached from the WAN side/Internet.
Imagine you have to access the LAN PC via SSH when you were on vacation.
If you could just enable the Port forwarding for SSH (port 22) in your modem to the Destination IP of 192.168.1.15 then the same PC can be accessed from Internet simply by accessing the ssh at 220.127.116.11 IP address. Modem will take care of the routing when it gets a TCP syn packet at its's WAN IP's 22 port.