Eventual consistency is a consistency model in which, after an update, a subsequent read may return the old value for some bounded period — but if no further writes occur, all replicas in the system are guaranteed to converge on the latest value. It is the price you pay for the availability and partition-tolerance side of the CAP theorem: a system that stays online during a network partition cannot, in general, also guarantee that every replica returns the same value at the same instant. DNS, S3 list-after-write, and most large-scale object stores are classically eventually consistent.
In a self-hosting context
Eventual consistency mostly matters when you self-host an object-storage cluster like MinIO, Garage, or SeaweedFS and treat it as a primary store: a freshly written object may briefly 404 or return a stale ETag from a different node. For everything that lives in a single Postgres or MySQL — the vast majority of self-hostable SaaS replacements in this directory — strict ACID semantics apply and eventual consistency does not enter the picture.