The autonomic (automatic) nervous system has two sub categories. First there is the sympathetic system which is responsible for arousal, alertness, emergencies, flight and fight response and stress. Second there is the parasympathetic system responsible for rest, digest, growth, repair, calm and vegetative functions. These systems tend to work in opposition.
An important aspect of meditation is to observe the interaction that exist between the sympathetic and the parasympathetic nervous system. A lot of the mental activity happening when we meditate (thoughts related to social fears) will trigger the sympathetic system. Therefore increasing our blood pressure and heart rate, tensing our muscles, dilating our bronchus (modifying our breath) etc. A great deal of what we call letting go in meditation is to stop the sympathetic nervous system and to reengage the parasympathetic system. It can easily be done by relaxing the mouth where the parasympathetic system has a lot of connections.
The autonomic nervous system has a high degree of plasticity. Through meditation and mindfulness we can manage to increase the facility with which the parasympathetic system engages. It would allow us to naturally become more relax in stressful situations resulting in better health but also in an increase of the usage of our prefrontal cortex. Thus in an increase of our abilties to reflect in difficult situations and act intelligently and appropriately instead of reacting emotionally and hurting ourselves and other people.