Networking concepts

Uses of a Firewall on a Router
Protects you from evildoers who try to control your computer over the Internet. Any service you expose to the Internet should be secured with a strong password.

Network Address Translation

There are not enough unique IP addresses to be able to connect all computers directly to the internet. Hence, to the outside world, all computers within a network are represented by the Gateway IP address.

Difference between Static, Dynamic & Overloading NAT

Static NAT is a one-to-one mapping, e.g an inside local address of 192.168.1.1 can translate to an outside local address of 62.253.258.6 (inefficient - you'll need n IP addresses for n internal machines). 

Dynamic is when you have a pool of available address to use as an outside local address, and internal clients simply use the first available address. Ideal when each client needs it's own internet presence but you want to share them out (useful when not all clients are online at the same time).

Overloading, also known as PAT (Port address translation), useful when you only have one outside local address in which all internal clients need to be seen by. Using PAT - each client can be assigned an individual socket (port\protocol\IP) and have that mapped to the single internet address. PAT is used on almost all home routers today.

References

[1] - Article from Kioskea.net on NAT, port forwarding & port trigg.