This is a great question and one that is not easily answered in a forum such as this. But, I'll do my best to be simple and concise.
Just as with anything it strength and conditioning, if you challenge the nervous system, it will improve. The motor units within the muscles will recruit muscle spindles as a higher and faster rate than before. Also, with training you will begin to create motor engrams, which are very specific neuro pathways that the body develops which use a short feedback loop within the spine instead of requiring feedback from the brain.
The key to developing the nervous system very quickly is to use "high neuro load" exercises. These exercises typically use a lot of different muscles simultaneously and will fatigue the athlete rather quickly. These exercises are typically thought of as "functional" and are very effective, but also can be difficult to learn and can expose a fatigued athlete to injury if you aren't careful.
