Stability is essentially defined as being able to keep things in neutral. Dynamic instability therefore has to do with being able to keep things in neutral while moving or, dynamically.
The sensitized nervous system is best understood with the fire station analogy. Consider an injury to be a fire, which sets off an alarm bell, pain. The longer the alarm is ringing, the more fire stations start ringing the alarm bell. Eventually, so many fire stations are involved that when the fire goes out (e.g., the injury heals), the fire alarm bells are still ring for almost no reason. What this ultimately means is that sensations not normally painful will be perceived by the body as pain.
At a certain point, pain becomes an emotional response to injury. The longer the pain goes on (i.e., months, years), the more true this is. Cognitive behavioral psychology has demonstrated that the way we think about things affects how we feel about them. What these two things mean together is that the response to pain is highly individual, and can help or hinder the healing process.
In the neck, and with headaches, there is a fourth perpetuating factor known as oculomotor dysfunction. The muscles at the base of the skull are wire together with the eye muscles for reflex movement. Injury, particularly due whiplash trauma in a motor vehicle accident, can disrupt these reflexes, forcing the head and neck to work much harder to move.