What is a loop-back address? 127.0.0.1 is a loop-back address, but what does this even mean? Please be very descriptive and give an example, as I'm having a hard-time understanding this.
The Wikipedia article on loopback puts it better than I could:
The term loopback (sometimes spelled loop-back) is generally used to describe methods or procedures of routing electronic signals, digital data streams, or other flows of items, from their originating facility quickly back to the same source entity without intentional processing or modification. This is primarily intended as a means of testing the transmission or transportation infrastructure.
In terms of IP addresses this means that any communications to that address effectively never leave or perhaps never actually enter your network interface card so that you always have a "connection".
This allows you to test client/server software (for example) with both parts running on the same machine.
A loopback address is "connected" to a virtual network card in your machine called the loopback adapter.
Anything sent to the virtual loopback adapter comes right back out of it. It's like it's "connected to itself."
For example, if I make a web request by typing "http://127.0.0.1/somesite.html" in my browser, that request goes through the (virtual) loopback adapter and then right back out of it.
So, if you have web server running on your system, and it's listening on 127.0.0.1, it will receive the request from your browser, and also be able to communicate with your browser by sending its response back to 127.0.0.1.
This is excellent for testing purposes, as you can see.
Nothing going through the loopback adapter goes out to the Internet, or leaves your system. The loopback adapter is completely contained within your system.
It simply means your local address. When you test your NIC, this can be done via "ping 127.0.0.1". When you do this you are testing to make sure that your information can go down to layer 1 and back up. If you suspect that your NIC is not working on a physical level, this makes a very good test.
It can also be used to specify to your applications that you do not want your information to leave the host computer. This can be seen when you have a server-client model application installed on the local computer, but you do not want that information to be accessible remotely. You can specify the server software to transfer information via the loopback address and your client software could listen in on the loop back address. This would provide the information to local applications, while disabling the ability for somebody else on a LAN to access whatever server software you set up as local.
I don't know if I explained it very well, but it was the best I could do. The Wikipedia Page has good information on it.