A blockchain is an append-only digital ledger storing a set of time-ordered transactions grouped in blocks that are linked together using cryptographic hashes.
Consensus emerges from independent verification of each transaction by each full node on the network. Blocks are added to blockchains through mining nodes at different intervals depending on the how the protocol determines validity of blocks, and the participants ability to create those new blocks. Nodes then verify the new blocks and construct the chain. Nodes then select which blockchain they prefer, typically based on cumulative proof-of-work demonstrated on the longest chain, and consensus emerges.