Monotonic reads is one of the session consistency guarantees defined for distributed systems. The rule is narrow but precise: within a single client session, reads progress forward in time. If you read version 5 of a record, no future read in that session can return version 4, 3, or anything older. It can return version 5 again, or version 6, or version 10, but never something staler than what you already saw.
It is important that this is a per-client guarantee, not a global one. Two different users can be looking at different versions of the same record at the same moment, and that is allowed. Monotonic reads only promises that any one client never witnesses time running backward for itself.
This is weaker than strong consistency. The system does not promise you see the latest write the instant it happens. It only promises you never regress. That makes it cheap enough to offer in systems that replicate data across many machines and regions, where strong consistency would be slow or impossible.