How A Ball Screw Works (Animated) 

This animation shows how a recirculating ball screw works. It is important to note that this has a external return tube and there are other designs and pathways, but they functionally all work the same. Not shown are the scrubbers which close in the mechanism on either end and which prevent debris from fouling the mechanism.
This was designed and animated in SolidWorks 2020. In total there are 70 bearing balls in this animation with each having its own path mate and path mate motor. (I would love if someday SolidWorks added 3D chains)
This animation was originally intended to be longer with it going back and forth a few times, but SolidWorks put up a good fight. Hopefully you still get the idea.