One of the most important problems that any payment network has to solve is double-spending. It is a fraudulent technique of spending the same amount twice. The traditional solution was a trusted third party - a central server - that kept records of the balances and transactions. However, this method always entailed an authority basically in control of your funds and with all your personal details on hand.
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.
Ethereum is also being used as a platform to launch other cryptocurrencies. Because of the ERC20 token standard defined by the Ethereum Foundation, other developers can issue their own versions of this token and raise funds with an initial coin offering (ICO). In this fundraising strategy, the issuers of the token set an amount they want to raise, offer it in a crowdsale, and receive Ether in exchange. Billions of dollars have been raised by ICOs on the Ethereum platform in the last two years, and one of the most valuable cryptocurrencies in the world, EOS, is an ERC20 token.
2) Pseudonymous: Neither transactions nor accounts are connected to real-world identities. You receive Bitcoins on so-called addresses, which are randomly seeming chains of around 30 characters. While it is usually possible to analyze the transaction flow, it is not necessarily possible to connect the real world identity of users with those addresses.