What are they and what are they used for?

Let me try to explain simply what proxies are by describing a scenario to you. 
Imagine this.  You need to call a scammer, but if you do he'll see your phone number and know where you live.  So what do you do?  You drive to the next town and use a phone box there.  Now if he traces the number, he'll only see the phone box you called from and not your house.

Now imagine the same thing, but this time you want to hide your location while sending an email to your scammer.  You go to the next town and use a computer there.  Again, if the scammer checks the location of where the email was sent from he'll see it was sent from a computer in the next town.

Let's think more globally now.  Imagine you could travel to somewhere the other side of the world to send that email.  Better yet, imagine you could write and send it from your PC, but then relay it from a computer the other side of the world to the scammer, so if he checks it'll only show the computer thousands of miles from you it was relayed from.

That's what we're talking about here.  The ability to use a program on the internet at your own location, but make it appear as if you're using a computer anywhere in the world.  Scammers use them to hide their location from the authorities.  Baiters use them to hide their location from scammers. 

"So how do I go about using proxies?" I hear you ask.

There are several different ways.  You can buy a program like HIDE IP PLATINUM to do the job or you can use Firefox plugins to do it.  Whichever method you use, you'll need a list of proxies.

Proxy lists are easy to find.  Just Google them.  Some proxies are free, some you have to pay for.  The choice is yours.  Just be aware of the dangers of using free, open proxies.  Some sites ban proxies, plus it can seriously slow your browsing down.  This is why we tell people that ask about Russian "ladies" using an "internet cafe" but having a proxy that it's a very good sign that they're dealing with a scammer.  What internet cafe would deliberately install a program that can slow the internet connection down?