If their relative speed to the air around them becomes low, the lift force will then decrease and the plane will fall back to earth because of gravity. One explanantion is to carrying-out a simple experiement. Put a piece of paper on a table. If you blow at it you can see that the paper is lifted off the table top. The harder you blow, the higher is the lifting of the paper.
Paper is definitely heavier than air.
Wings on the aircraft act like the paper. They generate lifting force when air is forced to flow over and under them. Shape of the wings is to ensure that the force generated is the highest possible.