I understand how bitcoin works but I'm finding it very hard to explain. It's so frustrating because when you mention "Digital Currency" to someone, you've got about 3 minutes to convince them it's not mickey mouse before they start wishing they were dead.http://en.wikipedia.org/wiki/Disney_dollar
Maybe Mickey Mouse is an approach to start with. Here you have a piece of paper marked with ink and sprinkled with glitter. If you take these to a Disney Theme Park in the U.S. you can use them to make purchases or to convert them at 1:1 of the denomination's face value for U.S. dollars.
These Disney Dollars are not representative currency. This is a private currency, backed by the trust that Walt Disney Company will accept them.
However, these bills are used as novelty gifts or collectors items, and will often trade (on eBay, for example) over face value. The true worth of these then is simply the amount that someone else is willing to pay to buy them.
Maybe that's a good way to start your explanation?