Plain English Meaning
When the wind is blowing from the side while you're taxiing, the airplane wants to turn and point itself into the wind, like a wind vane on a roof.
Full Definition
The tendency of an airplane on the ground to turn its nose into the wind when taxiing in a crosswind. It happens because the vertical tail surfaces present a larger side area behind the main wheels than the structure ahead of them, so the wind pushes the tail downwind and swings the nose upwind.
Context Anchor
Seen during taxiing, especially when wind is coming from the side and the airplane starts turning more than the pilot intended.
Derivation
From 'weather vane' -- the rooftop arrow that pivots so its pointer faces into the wind. The airplane behaves the same way on the ground, so pilots use the verb 'to weathervane' to the motion.