It's important to note that a consensus algorithm is made up of two parts:
Consensus; the generally accepted opinion or decision among a group of people/machines
Algorithm: A set of rules for accomplishing a task in a certain number of steps
When combined, you get a set of rules and a process, or steps, to accomplish a task in a generally accepted method.
Consensus Algorithms are a key component to blockchain as they provide the framework for the rules of the network that describe the sequence of events. Specifically, in blockchain we want a group of people/machines to agree that all transactions are validated and authentic.
Using a Consensus Algorithm you get a random network of machines to achieve consensus about transactions happening on the network. Without a "central authority" this is the accepted manner for verifying and vetting transactions on the network including prevention of double-spending.
Several consensus algorithms include Proof-of-Work (PoW), Proof-of-Stake (PoS), Delegated Proof-of-Stake (DPoS) and several others like Proof-of-Capacity, Proof-of-Authority, and DAG.