In plain English, under linearizability, writes should appear to be instantaneous. Imprecisely, once a write completes, all later reads (where “later” is defined by wall-clock start time) should return the value of that write or the value of a later write. Once a read returns a particular value, all later reads should return that value or the value of a later write.
From Section Linerizability(page 324), Chapter 9. Consistency and Consensus, Designing Data-Intensive Applications,
From Linearizability versus Serializability,