BitCoin is not so much a "currency" as an "emergent phenomenon". It makes things possible that have nothing to do with money.
For example, let’s say that you have a screen-play for a movie. Before shopping it around in Hollywood, you want to prove that it’s yours, so that a greedy producer can't steal it. Using BitCoin, you can add the signature (and date) of your screen-play to the "block chain", the "public ledger" where all Bitcoin transactions are stored. Now, if producers get greedy, you can (in theory) pull out this proof in a court and sue them.
As another example, let’s say that you have a great idea for a patent, but it’s not quite ready. Well, write it up into a file, then add the file’s signature to the block chain. Years from now, if somebody beats you to the patent filing, you can prove that you had the idea ahead of time.
You don’t need to really know how this works. There’s a website called http://proofofexistence.com that takes care of this for you. Put whatever it is you want in a file, the sign the file using that site. Years from now, you can prove to somebody then that this file existed right now, today.
This is just one example of many emergent phenomenon popping up around BitCoin. It’s not just about electronic currency, it’s about a lot of weird crypto concepts.