Observability is how well you can answer questions about a running system without shipping new code to investigate. It rests on three kinds of signal: logs (what happened), metrics (how much and how fast), and traces (the path a request took through the system). Together they let you move from "something is wrong" to "here is exactly what and where" quickly.
It is distinct from monitoring, which watches for known problems. Observability is about being able to diagnose the problems you did not anticipate, which, in a real system, are most of them. Building it in as features ship, rather than bolting it on after an outage, is the difference between a five-minute diagnosis and a five-hour one.