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.
^ "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

Most stock quote data provided by BATS. Market indices are shown in real time, except for the DJIA, which is delayed by two minutes. All times are ET. Disclaimer. Morningstar: © 2018 Morningstar, Inc. All Rights Reserved. Factset: FactSet Research Systems Inc. 2018. All rights reserved. Chicago Mercantile Association: Certain market data is the property of Chicago Mercantile Exchange Inc. and its licensors. All rights reserved. Dow Jones: The Dow Jones branded indices are proprietary to and are calculated, distributed and marketed by DJI Opco, a subsidiary of S&P Dow Jones Indices LLC and have been licensed for use to S&P Opco, LLC and CNN. Standard & Poor's and S&P are registered trademarks of Standard & Poor's Financial Services LLC and Dow Jones is a registered trademark of Dow Jones Trademark Holdings LLC. All content of the Dow Jones branded indices © S&P Dow Jones Indices LLC 2018 and/or its affiliates.
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.
The receiver of the first bitcoin transaction was cypherpunk Hal Finney, who had created the first reusable proof-of-work system (RPoW) in 2004.[28] Finney downloaded the bitcoin software on its release date, and on 12 January 2009 received ten bitcoins from Nakamoto.[29][30] Other early cypherpunk supporters were creators of bitcoin predecessors: Wei Dai, creator of b-money, and Nick Szabo, creator of bit gold.[25] In 2010, the first known commercial transaction using bitcoin occurred when programmer Laszlo Hanyecz bought two Papa John's pizzas for ₿10,000.[31]