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.
To realize digital cash you need a payment network with accounts, balances, and transaction. That‘s easy to understand. One major problem every payment network has to solve is to prevent the so-called double spending: to prevent that one entity spends the same amount twice. Usually, this is done by a central server who keeps record about the balances.
Ethereum-based customized software and networks, independent from the public Ethereum chain, are being tested by enterprise software companies.[47] Interested parties include Microsoft, IBM, JPMorgan Chase,[33][48] Deloitte,[49] R3,[50] Innovate UK (cross-border payments prototype).[51] Barclays, UBS and Credit Suisse are experimenting with Ethereum.
Using Ethereum’s “Turing complete” smart contract language, Solidity, developers are able to deploy a set of instructions to the blockchain that operate indefinitely with a high degree of finality and fraud-resistance. With the first block being mined in July 2015, Ethereum has since become the largest smart contract platform of its kind, and the second largest blockchain of all time as measured by market capitalization.

Bitcoin is a digital asset designed to work in peer-to-peer transactions as a currency.[4][141] Bitcoins have three qualities useful in a currency, according to The Economist in January 2015: they are "hard to earn, limited in supply and easy to verify."[142] Per some researchers, as of 2015, bitcoin functions more as a payment system than as a currency.[36]

Bitcoin is pseudonymous rather than anonymous in that the cryptocurrency within a wallet is not tied to people, but rather to one or more specific keys (or "addresses").[41] Thereby, bitcoin owners are not identifiable, but all transactions are publicly available in the blockchain. Still, cryptocurrency exchanges are often required by law to collect the personal information of their users.[citation needed]
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.
It takes a (global) village to raise a blockchain. The live network and the community of open source developers contribute significantly to this effort. They continuously refine and harden the Ethereum platform, helping it get faster at responding to industry demands for the value propositions it offers. These investments of time and resources speak to their faith in Ethereum governance and the value that businesses and developers see in its capabilities. – Joseph Lubin, CEO of Consensys

Homero Josh Garza, who founded the cryptocurrency startups GAW Miners and ZenMiner in 2014, acknowledged in a plea agreement that the companies were part of a pyramid scheme, and pleaded guilty to wire fraud in 2015. The U.S. Securities and Exchange Commission separately brought a civil enforcement action against Garza, who was eventually ordered to pay a judgment of $9.1 million plus $700,000 in interest. The SEC's complaint stated that Garza, through his companies, had fraudulently sold "investment contracts representing shares in the profits they claimed would be generated" from mining.[70]

In the blockchain, bitcoins are registered to bitcoin addresses. Creating a bitcoin address requires nothing more than picking a random valid private key and computing the corresponding bitcoin address. This computation can be done in a split second. But the reverse, computing the private key of a given bitcoin address, is mathematically unfeasible. Users can tell others or make public a bitcoin address without compromising its corresponding private key. Moreover, the number of valid private keys is so vast that it is extremely unlikely someone will compute a key-pair that is already in use and has funds. The vast number of valid private keys makes it unfeasible that brute force could be used to compromise a private key. To be able to spend their bitcoins, the owner must know the corresponding private key and digitally sign the transaction. The network verifies the signature using the public key; the private key is never revealed.[7]:ch. 5
Lightweight clients consult full clients to send and receive transactions without requiring a local copy of the entire blockchain (see simplified payment verification – SPV). This makes lightweight clients much faster to set up and allows them to be used on low-power, low-bandwidth devices such as smartphones. When using a lightweight wallet, however, the user must trust the server to a certain degree, as it can report faulty values back to the user. Lightweight clients follow the longest blockchain and do not ensure it is valid, requiring trust in miners.[101]
^ "Bitcoin: The Cryptoanarchists' Answer to Cash". IEEE Spectrum. Archived from the original on 4 June 2012. Around the same time, Nick Szabo, a computer scientist who now blogs about law and the history of money, was one of the first to imagine a new digital currency from the ground up. Although many consider his scheme, which he calls "bit gold", to be a precursor to Bitcoin
A cryptocurrency is a digital or virtual currency that uses cryptography for security. A cryptocurrency is difficult to counterfeit because of this security feature. Many cryptocurrencies are decentralized systems based on blockchain technology, a distributed ledger enforced by a disparate network of computers. A defining feature of a cryptocurrency, and arguably its biggest allure, is its organic nature; it is not issued by any central authority, rendering it theoretically immune to government interference or manipulation.
Blockchain analysts estimate that Nakamoto had mined about one million bitcoins[32] 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.[33][34] 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.[35][34]