Proprioception is the sense for the relation of body parts to each other. Proprioception allows us to touch our nose with the eyes closed, yet it also registers the effort required to perform an activity. Proprioceptive nerves start in the sensorimotor cortex (part of which is located in our spine) and end in the fascia around our organs and muscles, passing through a variety of relays. Proprioception interacts with our balance, but due to habitual misuse of the body this sense becomes very unreliable. As FM Alexander said, most people suffer from faulty sensory appreciation.
Sensory nerves register changes of their monitored modality. An object that moves fast in our direction captures automatically our attention, a hand touching us on the shoulder might remind us of the sensation of the fabric covering it. When we habitually overuse certain parts of the body, the proprioceptors initially send back information about this extra effort.
Our nervous systems adapts fast to the challenges it encounters, and parts of the body that mostly stopped to participate in the game of change become a bit like white spots on our body map. The body map itself, meaning our personal ideas about the location of joints and ranges of movement, quite often causes misuse.
The tactile information transmitted by the teacher's hands help recalibrating proprioception and our body map. The process of fine tuning of proprioception does not end with this recalibration, it just acts as a starting point to perceive the body state with more detail. However, Alexander Technique uses proprioception mainly to identify excessive effort rather than as feedback mechanism.