The simplest explanation for me comes from thinking of the cart running in flat-calm conditions.
Power is extracted from the wheels, which tends to slow the cart down, and fed to the propeller which pushes the cart forward.
If we imagine a cart with a 100% efficient propeller and transmission system, then the drag from the wheels would exactly balance the thrust from the prop. So (neglecting other drag and friction) the cart could run at any speed in any direction and would neither gain nor lose speed.
Of course, any real cart doesn't have a 100% efficient anything, so a real cart would quickly come to a standstill in calm conditions.
But any wind blowing adds to the thrust of the propeller - it does this because the prop can expend its power moving air at a lower speed - the power consumed by an ideal prop is the product of thrust and speed.
When the additional thrust generated by the prop in a wind is greater than the extra drag caused by all the real-world inefficiencies of the cart, then the cart accelerates until the thrust and drag once more become equal.