On 3 January 2009, the bitcoin network was created when Nakamoto mined the first block of the chain, known as the genesis block.[25][26] Embedded in the coinbase of this block was the text "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks".[16] This note references a headline published by The Times and has been interpreted as both a timestamp and a comment on the instability caused by fractional-reserve banking.[27]:18
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

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 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]