"What is needed is an electronic payment system based on cryptographic proof instead of trust."
First, Bitcoin nodes relay the transactions that they validate.
Second, Bitcoin uses a decentralized ledger technology also known as the Bitcoin blockchain which is a shared and public ledger where each and every transaction is recorded.
Third, the Bitcoin network is secured by a consensus algorithm named Proof-of-Work, which is defined as « a piece of data which is difficult (costly, time-consuming) to produce but easy for others to verify and which satisfies certain requirements. » (Wikipedia). Special nodes called miners allocate computing power to solve complex mathematical problems to validate transactions and discover new blocks. They compete to find it first, in order to obtain the reward of newly created bitcoins.
Last but not least, the users, who are contributing to the network by using it and sometimes fulfill one or more of the above mentioned functions. No single authority or individual has the power to take control of the network. Bitcoin is the first censorship-resistant, antifragile, peer-to-peer digital payment system. It is the most valued crypto-currency in the market with more than 40% market cap (July 2022 - Coin360).
