A Blockchain Consensus Algorithm determines how nodes in a blockchain network agree on the validity of transactions and the state of the distributed ledger. Popular algorithms include Proof of Work (PoW), where nodes compete to solve complex mathematical problems to add blocks, and Proof of Stake (PoS), where validators are chosen based on the amount of cryptocurrency they hold. Consensus algorithms are critical for ensuring the integrity and security of blockchain networks, providing a decentralized and trustless environment.