Power screws operate on the principle of converting rotational motion into linear motion, similar to a regular screw. The discussion touches on the analogy of a ship's propeller, comparing it to an inclined plane moving through water, which generates thrust. There are complexities involved, such as the stall angle affecting axial force production. One participant mentions having extensive notes on power screws from their Machine Design studies, indicating a willingness to share more detailed information. Overall, the conversation seeks to clarify the mechanics of power screws and their applications.