Kyle Kingsbury has a good look at linearizability and other forms of consistency: https://aphyr.com/posts/313-strong-consistency-models

distributed consensus is about having a group of processes agree on a single data value. For example, imagine you have a cluster of server. Each node has a replicated database.

(1) You want all your nodes to have the exact same replica of the database i.e consistency across your cluster.

You would need to reach consensus before any node actually adds anything to its local database to make sure that property (1) is fulfilled.

== Linearizability is just a consistency model i.e a variant of property 1 with stronger/weaker constraints.