Plain English Meaning
When a wing produces lift, each wingtip leaves a spinning trail of air behind it. If there is a crosswind, one of those trails gets pushed sideways with the wind. That one is called the downwind vortex.
Full Definition
The wingtip vortex that rotates in the same direction as a crosswind and therefore drifts downwind of the flight path that produced it. In a left crosswind, the right wingtip vortex becomes the downwind vortex; in a right crosswind, the left wingtip vortex does. It tends to move laterally away from the runway or track on the downwind side and may persist as a hazard to following aircraft.
Context Anchor
Seen in wake turbulence and discussions, especially when considering how move near a runway.