Vitalik Buterin picked the name Ethereum after browsing Wikipedia articles about elements and science fiction, when he found the name, noting, "I immediately realized that I liked it better than all of the other alternatives that I had seen; I suppose it was the fact that sounded nice and it had the word 'ether', referring to the hypothetical invisible medium that permeates the universe and allows light to travel."[9]

The “requesting a transaction” means you want to transfers some coins (let’s say bitcoin) to someone else. When you make the request the request is broadcasted to all the nodes. Then the nodes verify that (from all the history of transactions) you are not double spending your coins. When verified successfully the transaction is added in a block which is then mined by a miner. When the block is mined, your transaction is confirmed and the coins are transfered.
The overwhelming majority of bitcoin transactions take place on a cryptocurrency exchange, rather than being used in transactions with merchants.[146] Delays processing payments through the blockchain of about ten minutes make bitcoin use very difficult in a retail setting. Prices are not usually quoted in units of bitcoin and many trades involve one, or sometimes two, conversions into conventional currencies.[36] Merchants that do accept bitcoin payments may use payment service providers to perform the conversions.[147]
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.
Within a cryptocurrency network, only miners can confirm transactions by solving a cryptographic puzzle. They take transactions, mark them as legitimate and spread them across the network. Afterwards, every node of the network adds it to its database. Once the transaction is confirmed it becomes unforgeable and irreversible and a miner receives a reward, plus the transaction fees.
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.  
“A DAO consists of one or more contracts and could be funded by a group of like-minded individuals. A DAO operates completely transparently and completely independently of any human intervention, including its original creators. A DAO will stay on the network as long as it covers its survival costs and provides a useful service to its customer base” Stephen Tual, Slock.it Founder, former CCO Ethereum.

Cryptocurrencies are digital gold. Sound money that is secure from political influence. Money that promises to preserve and increase its value over time. Cryptocurrencies are also a fast and comfortable means of payment with a worldwide scope, and they are private and anonymous enough to serve as a means of payment for black markets and any other outlawed economic activity.

“In 2 years from now, I believe cryptocurrencies will be gaining legitimacy as a protocol for business transactions, micropayments, and overtaking Western Union as the preferred remittance tool. Regarding business transactions – you’ll see two paths: There will be financial businesses which use it for it’s no fee, nearly-instant ability to move any amount of money around, and there will be those that utilize it for its blockchain technology. Blockchain technology provides the largest benefit with trustless auditing, single source of truth, smart contracts, and color coins.”
This flexibility makes Ethereum the perfect instrument for blockchain -application. But it comes at a cost. After the Hack of the DAO – an Ethereum based smart contract – the developers decided to do a hard fork without consensus, which resulted in the emerge of Ethereum Classic. Besides this, there are several clones of Ethereum, and Ethereum itself is a host of several Tokens like DigixDAO and Augur. This makes Ethereum more a family of cryptocurrencies than a single currency.
Network nodes can validate transactions, add them to their copy of the ledger, and then broadcast these ledger additions to other nodes. To achieve independent verification of the chain of ownership each network node stores its own copy of the blockchain.[80] About every 10 minutes, a new group of accepted transactions, called a block, is created, added to the blockchain, and quickly published to all nodes, without requiring central oversight. This allows bitcoin software to determine when a particular bitcoin was spent, which is needed to prevent double-spending. A conventional ledger records the transfers of actual bills or promissory notes that exist apart from it, but the blockchain is the only place that bitcoins can be said to exist in the form of unspent outputs of transactions.[7]:ch. 5
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