In the diagram below showing a spinning ball or tube (see video for both examples) the stream of air rushing past tends to cling to the spinning ball or tube and so it deflects the stream of air downwards. The force pushing the air down results in an equal and opposite force pushing the tube up. That effect is described by Newton's Third Law that every action has an equal and opposite reaction. This reaction is called the Magnus force.

At the top the rotation is away from the direction of flight so the speed of the air relative to the surface is low and so the air tends to stick to the surface. and much of it is deflected down.

At the the bottom edge, as it appears in the diagram, the spin is towards the motion through the air. That  bottom edge is moving faster relative to the air so the stream breaks away. This produces turbulence behind the ball and the air is not deflected very much. The overall force on the ball therefore comes from the air being deflected down and so the ball is pushed up.

There is a more thorough explanation with practical examples in the video below: