Plain English Meaning
When a wing produces lift, air under the wing pushes up and around the tip into the area above the wing. That sideways spill gets dragged backward as the aircraft moves forward, leaving a pair of spinning air tubes behind the wingtips.
Full Definition
A wingtip vortex is a swirling, tube-shaped mass of air that trails behind each wingtip of an aircraft in flight. It forms because high-pressure air beneath the wing spills around the wingtip into the lower-pressure air above the wing, creating a rotating flow that streams aft. Wingtip vortices are strongest when the aircraft is heavy, slow, and in a clean configuration (gear and flaps up).