Acharya Prashant explains that the mind is not an independent entity but rather a shadow of the 'I' or the ego (Aham). Just as a shadow follows the movement of the body, the mind follows the definitions and beliefs that the ego holds about itself. If the ego establishes itself in a place of impurity or ignorance, the mind will naturally reflect that impurity. Therefore, trying to clean or control the mind without addressing the ego is a futile exercise, similar to trying to clean a shadow while standing in mud.