Lets start simply. You are reading this webpage through a link called guru3d.com, this link relates to an ip address (if you don't believe me, open a dos / command prompt and type ping guru3d.com). The ip address relates back to a physical machine in the world which hosts this text. Your computer has a very similar setup.

The way your PC connects to guru, is through (amongst other things) routers. You are connected to your ISP through cable/dsl/dialup, now I pretty much guarantee that you are then passed through some form of router, which combines you and everyone else connected to the ISP, into another ip address. This (very simplified model) happens in both directions between you and guru3d. This process is called network address translation or NAT, and can be found in every off the shelf router. One last point about NAT is that there are two sides to it. The local side, and the world side. You are on the local side of your ISP, and guru is on the world side of your ISP. When you get a router, you will be on the local side of the router, guru (and your ISP) will be on the world side of your router. The local side is referred to as the LAN side (local area network) while the world side is referred to as the WAN side (Wide area network).

e.g. PC A (192.168.0.1) <----> (192.168.0.254 - LAN Side) Router (38.22.22.1 - WAN Side) <----> Internet

NAT can be built on to provide various options that can be adjusted inside a router, and depending on how complex the designers of the hardware are, many administration functions are born e.g. Blocking access to the internet for certain machines on your network.

NAT is often referred to as a hardware firewall, this is my pet hate as NAT is NOT a firewall. Pure NAT does protect your machine from attacks, but only because the attacker does not have the required information to locate your machine. i.e. The attacker may have your routers address of 38.22.22.1, but hasn't got the routing information to get to your 192.etc address. A firewall can often be included in your router, however referring to NAT as a firewall is wrong (Rant over !).