Consensus
In short: Consensus is the agreement among network participants about which transactions are valid and in what order they are added to the blockchain.
Consensus is the agreement among network participants about which transactions are valid and in what order they are added to the blockchain. The rules a network uses to reach that agreement are called its consensus mechanism.
Why it matters
A public blockchain has no central bank or server to decide who owns what, so many independent nodes must end up with the same copy of the ledger. Consensus is what prevents the same coins from being spent twice and makes rewriting past blocks very expensive. Well-known mechanisms include proof of work, where miners spend computing power, and proof of stake, where validators lock up coins as collateral. It is also why exchanges wait for a number of block confirmations before crediting a deposit.
Example
Two Bitcoin miners find a valid block at almost the same moment, so for a short time the network sees two competing versions of the chain. Each miner keeps building on the version it received first. As soon as one branch gets the next block, it carries more accumulated work, every node switches to it, and transactions from the abandoned block go back to waiting for confirmation.