Bitcoin’s consensus rules are written into each Bitcoin full node implementation. When a transaction is made, full nodes on the network are able to check the transaction against these written rules which state that:
1) transactions must have correct signatures that match the address from which BTC is spent, 2) transactions are in the correct data format, and that 3) transactions are not a double-spend.
After transactions are broadcast as valid, they are able to enter the mempool where they await inclusion into the next available block. Blocks are confirmed every 10 minutes on the Bitcoin blockchain by the network of miners which use Proof-of-Work.
Miners employ physical hardware that aims to solve a mathematical “proof”. On the Bitcoin network, miners use a special kind of hardware called an ASIC, or Application Specific Integrated Circuit. These chips are designed to execute any one function that they are programmed for.
In this case, they are directed towards securing the Bitcoin network by solving mathematical proofs that serve as the basis for PoW. Miners join together forming pools in which they aggregate their computing resources to compete against other miners and pools, as they are all in a competition to solve the “proof”- more participation leads to increasing network difficulty.
The race to stay ahead of this network difficulty to solve these proofs is what is regarded as the “work”- miners must expend capital for hardware and electricity if they want to remain profitable.
Upon completion of the proof, transactions are hashed into blocks using the SHA-256 algorithm, and “mined” BTC is rewarded to pools in proportion to their contribution towards solving proofs every 10 minutes. Bitcoin is widely regarded as immutable because of how network incentives are aligned with PoW.