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.
Blockchains are secure by design and are an example of a distributed computing system with high Byzantine fault tolerance. Decentralized consensus has therefore been achieved with a blockchain. Blockchains solve the double-spending problem without the need of a trusted authority or central server, assuming no 51% attack (that has worked against several cryptocurrencies).
The validity of each cryptocurrency's coins is provided by a blockchain. A blockchain is a continuously growing list of records, called blocks, which are linked and secured using cryptography. Each block typically contains a hash pointer as a link to a previous block, a timestamp and transaction data. By design, blockchains are inherently resistant to modification of the data. It is "an open, distributed ledger that can record transactions between two parties efficiently and in a verifiable and permanent way". For use as a distributed ledger, a blockchain is typically managed by a peer-to-peer network collectively adhering to a protocol for validating new blocks. Once recorded, the data in any given block cannot be altered retroactively without the alteration of all subsequent blocks, which requires collusion of the network majority.
Like other blockchains, Ethereum has a native cryptocurrency called Ether (ETH). ETH is digital money. If you’ve heard of Bitcoin, ETH has many of the same features. It is purely digital, and can be sent to anyone anywhere in the world instantly. The supply of ETH isn’t controlled by any government or company - it is decentralized, and it is scarce. People all over the world use ETH to make payments, as a store of value, or as collateral.
The overwhelming majority of bitcoin transactions take place on a cryptocurrency exchange, rather than being used in transactions with merchants. 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. Merchants that do accept bitcoin payments may use payment service providers to perform the conversions.
There are many ways you can plug into the Ethereum network, one of the easiest ways is to use its native Mist browser. Mist provides a user-friendly interface & digital wallet for users to trade & store Ether as well as write, manage, deploy and use smart contracts. Like web browsers give access and help people navigate the internet, Mist provides a portal into the world of decentralized blockchain applications.
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.
Bitcoin (BTC) is a consensus network that enables a new payment system and a completely digital currency. Powered by its users, it is a peer to peer payment network that requires no central authority to operate. On October 31st, 2008, an individual or group of individuals operating under the pseudonym "Satoshi Nakamoto" published the Bitcoin Whitepaper and described it as: "a purely peer-to-peer version of electronic cash, which would allow online payments to be sent directly from one party to another without going through a financial institution."
Third-party internet services called online wallets offer similar functionality but may be easier to use. In this case, credentials to access funds are stored with the online wallet provider rather than on the user's hardware. As a result, the user must have complete trust in the online wallet provider. A malicious provider or a breach in server security may cause entrusted bitcoins to be stolen. An example of such a security breach occurred with Mt. Gox in 2011.
Blockchain analysts estimate that Nakamoto had mined about one million bitcoins before disappearing in 2010, when he handed the network alert key and control of the code repository over to Gavin Andresen. Andresen later became lead developer at the Bitcoin Foundation. Andresen then sought to decentralize control. This left opportunity for controversy to develop over the future development path of bitcoin, in contrast to the perceived authority of Nakamoto's contributions.