Plain English Meaning
The strongest sideways wind that test pilots actually proved the airplane could handle during takeoff and landing testing. It is a reference number, not a hard limit.
Full Definition
The highest crosswind component at 90 degrees to the runway that was actually flown and proven controllable during the airplane's certification testing. It is published in the Pilot's Operating Handbook and reflects what the test pilot demonstrated, not a structural limit or a guaranteed maximum capability.
Context Anchor
You will see this term when checking an airplane’s handbook before deciding whether the wind is acceptable for takeoff or landing.
Derivation
Demonstrated' means 'shown to be true through action.' The number was shown to during testing — it was not calculated or . That is why it is called demonstrated rather than maximum.