Plain English Meaning
When the wind blows across the runway instead of straight down it, two things happen on takeoff and landing: the airplane gets pushed sideways, and its nose tries to swing into the wind. The pilot has to actively counter both with the controls.
Full Definition
The tendency of an airplane to drift sideways and to weathervane into the wind during takeoff and landing when the wind has a component blowing across the runway rather than directly down it. The drift component pushes the airplane sideways through the air, while the weathervaning component yaws the nose toward the wind because the larger surface area behind the main gear (fuselage and tail) acts like a weather vane.
Context Anchor
Encountered during , especially as the airplane transitions from on the runway to flying just above it.