A cryptocurrency is essentially a shared ledger secured by cryptography. Researchers have been trying to create digital money for more than 40 years. The main sticking point is that there needed to be a central authority to issue the money and then to validate transactions to prevent counterfeiting and spending of duplicate money. The government shut down several companies that attempted to implement a digital money system.
In 2008, a white paper was published describing a money system that could issue money and provide the transaction clearing function without requiring a central authority. The system described, Bitcoin, was put into operation on January 3, 2009 and has been running ever since. As there is no central company running the system (it is a peer to peer network), there is no way for government to easily shut it down.
Over the last nine years, a lot of infrastructure has grown up around cryptocurrencies. There are currency exchanges that allow converting between government money and cryptocurrencies (there are many of them now beside Bitcoin), payment processors to allow businesses to accept crypto for goods and services, etc.
While the initial implementations of these shared ledgers was for digital currencies, the ledgers can be used to account for other things. Digital assets representing ownership of other things of value like stocks or real estate are being implemented.
An Initial Coin Offering (ICO) is one such digital asset. You can think of the ICO as representing shares in a company, and they are being used to raise money for start ups. As you might imagine, the SEC and other government regulators are taking a hard look at ICOs as well as non-government issued currencies.
So that’s a bare bones description. There’s lots of detail we could get into. I can try to answer questions if there are any.
On Sept 22, the Wall Street Journal published an interview with Balaji Srinivasan, who said that "The Blockchain Is the Internet of Money.” I’d link to it, but it’s behind a paywall. On the subject of China’s recent actions on cryptocurrencies, Srinivasan pointed out that China is something of a technocracy; people with serious tech chops are actually influential in the government. Whereas in the US, well, we’re more of an ignorocracy. :-/He thinks the upshot will be that China will come out with its own digital currency linked to the currency of China, that there will be a competition.