Money exists so that people who don't trust each other can conduct business together. In order for that business to happen, there needs to be something in the middle that they both trust. Traditionally, that "something in the middle" has been a bank and/or government. Contracts are the same way - in order for two parties to overcome their individual distrust, they both had to trust something bigger in between.

Bitcoin uses math and distributed computing to make that "something in the middle" a faceless, anonymous crowd while maintaining the trust. Unfortunately there are problems with the math and distributed computing that is already crippling the ability of Bitcoin to be "something in the middle" for more than the lunatic fringe that is already using it. Still more unfortunately, the people who are helping to shape Bitcoin aren't cooperating very well and the trust is eroding somewhat.

Ethereum is an idea similar to Bitcoin, but there are no design flaws that will eventually lead to the problems Bitcoin has right now. Because of this, the techno-nerds who like the idea of cryptocurrency for what it means for innovation prefer Ethereum. There has been substantial excitement this week over the sour grapes departure of one of the main Bitcoin developers, which has caused Ethereum to go up in value by about 150%. And yes, you can mine it but because it is a more clever protocol, it puts a substantial load on your GPU. Therefore, archetypal BTC miners won't work.