The human body can be thought of as an impossibly complex matrix of muscles and sinew, interwoven with nerves that report back, in detail so excruciating it puts even our best processors to shame, to the central nervous system, the brain and the nerve ganglions in the spine. This incredible mass of information processing equipment is all set atop an interior form, your skeleton. This incredible frame is also full of surprises and is a great thing indeed. Keeping the skeleton in a certain condition or position will have results all throughout the body. This is why misalignment and improper posture can radiate or cause pain in places that are quite separate and apart from the initial site of the problem.
The jaws are one of these places that can end up causing pain in all sorts of areas that you would not believe. The jawbone is connected to the neck bone and to several vertebrae in the spine, and if misaligned, this can put these vertebrae and the neck as well in a particularly painful spot. This can lead to improper posture to compensate for the unnatural angle of the neck, which will cause pain in the spine, in the neck and possibly a bunch of other places along the back and in the spine.
The same thing is true conversely speaking. If you have bad posture because of a crooked spine or because of some sort of skeletal irregularity, that may affect your bite and the way your jaw stands, which can cause TMJ problems or damage to your teeth if they are locking improperly and scraping against each other.
The relationship between your posture and your teeth is a reciprocal relationship, and as such incredibly complicated. This is why orthodontics can cause head and neck pains at first, or may solve them, and the tightness you feel in your teeth and mouth can cause pain and tightness elsewhere in the body as well.
Orthodontics can help even out your bite and align the jaws. This can also force a change of posture, as the posture your body assumed in order to escape the pain of maladjustment will no longer be comfortable now that pressure is being exerted to straighten out the cause of your improper posture. In this way, orthodontics can help your posture.