The right-handed screw rule is a method to determine the direction of rotation and movement for screws and vectors. By curling the fingers of the right hand in the direction of rotation, the thumb indicates the direction of the screw's advancement. This rule applies universally across various systems, emphasizing the importance of a consistent frame of reference when discussing rotational motion. In a right-handed coordinate system, a screw moving from vector A to vector B advances in the direction of vector C. Understanding this concept is crucial for accurately applying rotational mechanics in physics and engineering.