Many traditions across the world state that humans have a sort of subtle body that is part of the physical body, and/or is a non-physical projection of the physical body. This subtle body can travel into different places or dimensions in some traditions, while in other traditions, like Chinese holistic medicine, one can affect the subtle body and thereby affect the phsyical body. Affecting the physical body through the subtle body can be done through acupuncture, meditation, or other means. In western traditions the subtle body is known as the astral body. In Tantric Hindu and Tantric Buddhist (Vajrayana) tradition there are subtle energy centers in the subtle body called 'Chakras', which literally translates to 'wheels'. These chakras can be manipulated through meditation and visualization. Focusing on certain parts of the body during meditation can activate the chakras. All of the the traditions that espouse the notion of a subtle body believe that the subtle body is connected to the mind in some way.
While the idea of a subtle body may sound far-fetched and unproven, there are examples of physiology and experiences that seem to validate this sort of conception; the concept of the subtle body may be based in science. Clinical evidence points to the fact that nearly all experienced pain and sensory information is done so through the brain. The pain experienced by phantom limbs and the sensation of a phantom limb itself is explained by the subtle body, although not scientifically. A scientific explanation that is a counterpart to the idea of a subtle body that can explain phantom limbs and their pain has emerged in science, and it is called the neuromatrix. The neuromatrix is like a subtle body, named the body-self, that each person is born with that feels the pain, sensations, and all of the qualities of experience of the body. The neuromatrix for the body-self is spread all throughout selective areas of the brain. The neuromatrix is also modified by experience and the conscious mind itself. There is some evidence that points to the neuromatrix as the correct theory regarding phantom limbs and sensory expeirence in general. Firstly, paraplegics report fatigue in their legs after persistent bicycling movements, and, likewise, fatigue exists in a tightly clenched fist by arm amputees. Secondly, the brain generates perceptual experience even when physical stimuli are not there. Thirdly, people who are born without limbs, or who have lost limbs at an early age, still have phantom limbs and phantom limb sensations. Finally, another phenomenon unexplained by normal stimulus-response type theories of pain that is explained by the neuromatrix theory of pain is how women giving birth can either have in labor pain or pleasure. The experiences that women have in labor are the same, although the sensational experiences vary. All of these phenomena are evidence for the neuromatrix theory of pain and sensory experience.
Although the neuromatrix theory accounts for pain and phantom limbs, and was preceded in a similar manner by speculation of the existence of a subtle body, even some things in experience are still somewhat unexplained by science that are still explained by the existence of a type of subtle body, which might also be accounted for in the neuromatrix theory of pain. An example of this would be analgesia that occurs by acupuncture and acupressure. In the Chinese theory of acupuncture and acupressure, in the body there are lines where a type of energy travels, and these lines are called meridians, similar to the idea of energy centers called chakras. One of the strangest things about acupuncture is that it produces an effect on one part of the body while another distant and unrelated part of the body is being stimulated. While it is known that pain can occur in one part of the body due to stimulation of another part of the body, it is unknown how this happens or why. It is also unknown how stimuli can produce or relieve pain not just between long distances, but long times. So far no theory of pain can sufficienty explain how analgesia by acupuncture occurs over these distances and times. One might speculate that in the neuromatrix theory of pain the body-self has certain properties such that physical stimulation in one part of the body may affect another part of the body-self, such that a feeling or sensation occurs in the body-self. In fact, the neuromatrix theory doesn't just account for immediate sensations in the body-self, but also for cultural factors, the experient's emotional state, stress, cognitive input, and more.
TL;DR - The neuromatrix theory of pain is the modern scientific counterpart to the traditional and somewhat ancient concept of the subtle body.