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.
In March 2017, various blockchain start-ups, research groups, and Fortune 500 companies announced the creation of the Enterprise Ethereum Alliance (EEA) with 30 founding members.[16] By May, the nonprofit organization had 116 enterprise members—including ConsenSys, CME Group, Cornell University's research group, Toyota Research Institute, Samsung SDS, Microsoft, Intel, J. P. Morgan, Cooley LLP, Merck KGaA, DTCC, Deloitte, Accenture, Banco Santander, BNY Mellon, ING, and National Bank of Canada.[17][18][19] By July 2017, there were over 150 members in the alliance, including recent additions MasterCard, Cisco Systems, Sberbank and Scotiabank.[20][21]
Armed with the knowledge of Ethereum’s price history, future predictions and the associated risks to investing in this cryptocurrency, you may now be considering a purchase. Buying Ethereum has evolved from a niche and slightly cumbersome process to one which has been polished into simplicity. Ethereum can now be bought through debit/credit card, epayment platforms, bank transfer, cash or even Bitcoin and other cryptocurrencies. Speculators can bet on the asset (both long and short) through “contracts for difference” (CFDs) or they can purchase and secure the asset themselves to “become their own bank”.

The term altcoin has various similar definitions. Stephanie Yang of The Wall Street Journal defined altcoins as "alternative digital currencies,"[20] while Paul Vigna, also of The Wall Street Journal, described altcoins as alternative versions of bitcoin.[21] Aaron Hankins of the MarketWatch refers to any cryptocurrencies other than bitcoin as altcoins.[22]

Ethereum can also be used to build Decentralized Autonomous Organizations (DAO). A DAO is fully autonomous, decentralized organization with no single leader. DAO’s are run by programming code, on a collection of smart contracts written on the Ethereum blockchain. The code is designed to replace the rules and structure of a traditional organization, eliminating the need for people and centralized control. A DAO is owned by everyone who purchases tokens, but instead of each token equating to equity shares & ownership, tokens act as contributions that give people voting rights.

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).
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.
A cryptocurrency (or crypto currency) is a digital asset designed to work as a medium of exchange that uses strong cryptography to secure financial transactions, control the creation of additional units, and verify the transfer of assets.[1][2][3] Cryptocurrencies use decentralized control as opposed to centralized digital currency and central banking systems.[4]

Essentially, any cryptocurrency network is based on the absolute consensus of all the participants regarding the legitimacy of balances and transactions. If nodes of the network disagree on a single balance, the system would basically break. However, there are a lot of rules pre-built and programmed into the network that prevents this from happening.
Bitcoin has been criticized for its use in illegal transactions, its high electricity consumption, price volatility, and thefts from exchanges. Some noted economists, including several Nobel laureates, have characterized it as a speculative bubble. Bitcoin has also been used as an investment, although several regulatory agencies have issued investor alerts about bitcoin.[19][20]