Bitcoin
Bitcoin is an electronic currency that is not issued by any central bank. The advantage is that it lets people do anonymous transactions, and can't be inflated/deflated by governments. It is designed to be a scarce resource, like gold. That is how it keeps it's value.
The ways to get it:
1. Buy or sell it (by exchanging for dollars) through a bitcoin exchange. You have to have a "wallet", which is a program designed to store your bitcoin.
2. Some merchants accept bitcoin directly. So you transfer it wallet-to-wallet.
3. "Mine" it. This is how it keeps it's scarcity. As each bitcoin gets "mined", it gets harder to create more (uses more computer time and power). Bitcoin "mining" means your computer doing a complex calculation, which gets harder as more bitcoin is created in the world.
Blockchain
The really valuable thing about bitcoin is the concept of the "blockchain". This is a ledger that is on millions of computers. Every time a bitcoin transaction occurs anywhere in the world, it is simultaneously recorded in every copy of the blockchain, so it can't be counterfeited.
This is a hot area in finance/IT, because they can extend blockchains for other applications. For example, real estate. You could record real estate transactions in a blockchain, and wouldn't need courthouse records or titles.
Ethernium, is the second most popular electronic currency, and it takes the blockchain concept further in that you can program the blockchain to do certain things when a transaction occurs. So, in finance, they can make smart contracts where, for example, a bond is stored in a blockchain and, when a transaction occurs, automatically release a payment.
Government View
Governments don't like bitcoin because:
1. Transactions are anonymous.
2. It's being used online by hackers and drug dealers.
3. They also talk about banning paper bills such as $100 and 100 euro notes. So, they want people to use payment systems that use paper trails, so they can go after terrorists, tax evaders, and money launderers.
But, governments do support research into blockchain technology. For example, the Federal Reserve may eventually use a blockchain to clear checks faster.
Hacking / Mining
One of the latest twists is hackers creating malware that cause infected computers to mine for bitcoin in the background. So, they are stealing your computing resources to create more bitcoin for themselves.
Initial Coin Offerings (ICOs)
Another big trend right now is for coin-based startups do raise money through "Initial Coin Offerings" (ICOs), which are unregulated by the SEC (though the Chinese Central Bank recently banned them, causing a temporary fall in the price of Ethereum and Bitcoin.)
Many of these coin start-ups are offering alternatives to bitcoin (i.e. they are pure currencies). Others work off of Ethereum, since they are smart-contract enabled, to offer services.
For example, one company is called The Golem Project, and they aim to create a super computer out of people's computers. So, they created a coin called GNT. When you allow the Golem network to use your computer resources, you get paid in GNT. When you want to use the super computer, you pay in GNT.
To start up, they sold GNT tokens that had to be paid for in cash or bitcoin (BTC).
"The ICO was restricted on 820,000,000 tokens, for which the developers received more than 10,000 BTC. Today the market share of Golem is beyond 50,000 BTC." (https://blockgeeks.com/guides/what-is-an-initial-coin-offering/)
