Consensus is the process by which a majority opinion is reached by everyone who is involved in running the blockchain. Agreement must be made on which blocks to produce, which chain to adopt, and to determine the single state of the network. The consensus protocol determines how individual nodes assess the current state of the ledger system and reach a consensus. It has three main responsibilities; to perform a leader check and decide if a block should be produced, to handle chain selection, and to verify blocks that are produced.
Blockchains create consensus by allowing participants to bundle transactions that others have submitted to the system in blocks, and add them to their chain (sequence of blocks). Determining who is allowed to produce a block when, and what to do in case of conflicts, (such as two participants adding different blocks at the same point of the chain), is the purpose of the different consensus protocols. Our ground-breaking proof-of-stake consensus protocol Ouroboros is proven to have the same security guarantees that proof of work has. Rigorous security guarantees are established by Ouroboros and it was delivered with several peer-reviewed papers that were presented in top-tier conferences and publications in the area of cybersecurity and cryptography. Different implementations of Ouroboros have been developed. For further details on each flavour of Ouroboros, you can read the technical specifications for Classic, Byzantine Fault Tolerance (BFT), Genesis, Praos, and more recently the scalability solution Hydra.