Acharya Prashant explains the relationship between desire and rebirth as described in the Mundaka Upanishad. He clarifies that rebirth is not a mystical event but a psychological process where one assumes a specific persona to fulfill a desire. Every desire requires an individual to become something else, thereby condemning them to a future role and preventing the 'checkout' or liberation from the current state. He emphasizes that desires lack inherent longevity and only persist because we provide them energy through association and fear. By observing a desire without acting upon it, one can see it fade away naturally like a wave ebbing out.