You don‘t need to understand the details about SHA 256. It‘s only important you know that it can be the basis of a cryptologic puzzle the miners compete to solve. After finding a solution, a miner can build a block and add it to the blockchain. As an incentive, he has the right to add a so-called coinbase transaction that gives him a specific number of Bitcoins. This is the only way to create valid Bitcoins.
Full clients verify transactions directly by downloading a full copy of the blockchain (over 150 GB As of January 2018). They are the most secure and reliable way of using the network, as trust in external parties is not required. Full clients check the validity of mined blocks, preventing them from transacting on a chain that breaks or alters network rules.:ch. 1 Because of its size and complexity, downloading and verifying the entire blockchain is not suitable for all computing devices.
In the end, the majority of the Ethereum community voted to perform a hard fork, and retrieve The DAO investors money. But not everyone agreed with this course of action. This resulted in a split where two parallel blockchains now exist. For those members who strongly disagree with any changes to the blockchain even when hacking occurs there is Ethereum classic. For the majority who agreed to rewrite a small part of the blockchain and return the stolen money to their owners, there is Ethereum.
The first cryptocurrency to capture the public imagination was Bitcoin, which was launched in 2009 by an individual or group known under the pseudonym, Satoshi Nakamoto. As of February 2019, there were over 17.53 million bitcoins in circulation with a total market value of around $63 billion (although the market price of bitcoin can fluctuate quite a bit). Bitcoin's success has spawned a number of competing cryptocurrencies, known as "altcoins" such as Litecoin, Namecoin and Peercoin, as well as Ethereum, EOS, and Cardano. Today, there are literally thousands of cryptocurrencies in existence, with an aggregate market value of over $120 billion (Bitcoin currently represents more than 50% of the total value).