Plain English Meaning
It is the smooth, curved leveling-off the pilot makes a few feet above the runway, easing the nose up so the airplane stops descending sharply and settles softly onto its main wheels.
Full Definition
The round out (also called the flare) is the maneuver performed just before touchdown in which the pilot smoothly transitions the airplane from the descending approach attitude to a nose-slightly-high landing attitude, gradually reducing the rate of descent so the wheels meet the runway gently rather than at the full descent speed.
Context Anchor
You encounter round out during the final moments of a normal landing, after the and before the wheels touch the runway.