There are two branches of the autonomic nervous system, namely the sympathetic nervous system and the parasympathetic nervous systems. Both of which regulates bodily functions involuntarily but in different manners. The parasympathetic system is the system primarily activated in "relaxed" states or "rest and digest" states. These include digestion, urination, slowing of heart rate, slowing of respiratory rate, etc. The sympathetic nervous system on the other hand is primarily activated by "flight or flight" response such as rage or fear. These include inhibition of digestion, increase in heart rate and respiratory rate, sweating, etc.
Aerobic exercise is the body producing energy WITH the use of oxygen (light activities like jogging). Anaerobic exercise produce energy without the use of oxygen and is typically a higher intensity that burns fat AND helps gain lean muscle mass (these are activities like weight lifting).