The relaxed feeling one gets from acupuncture comes from sedation of the sympathetic nervous system, or the "flight or fight response". This helps de-stress, and physiologically improves blood circulation, muscle tightness and digestion, just to name a few.
Acupuncture has also been shown to affect a wide variety of hormones including those that control ovulation and menstruation due to its effect on the hypothalamus-pituitary-ovarian axis (HPOA)
Acupuncture affects neurochemicals such as serotonin that, among other things, affect mood and mental states.
It is not just any acu-points that will have these effects. The ancients knew that specific acu-points were indicated for specific functions. Research with real time fMRI of the brain have demonstrated that the classic indications for points are accurate. For example, a point two inches above the wrist on the top side of the forearm (SJ5) is classically recommended for hearing problems. When this point is stimulated it strongly affects the audio cortex. This kind of research has been done on many specific points based on classic indications.