The use of the term acupressure massage isn't accurate because acupressure isn't massage in the Western sense.
Acupressure is an Asian bodywork therapy based on the same energy principles used in acupuncture. Practitioners use pressure instead of needles on the points (acupoints) along energy lines (meridians) to promote the flow of energy in your body.
According to Traditional Chinese Medicine, life energy (chi or qi) flows through the meridians. In a healthy person, the energy flows freely, while blocked energy leads to illness.
Pressing acupoints may stimulate the body's natural self-healing abilities by reducing tension, increasing circulation, and helping your body relax. Research suggests that stimulation of acupoints increases release of endorphins.
Using pressure on acupoints can potentially help many problems, including headaches, back problems, and menstrual cramping, and may also boost the immune system.
The most well-known type of acupressure is shiatsu, which originated in Japan. Shiatsu can be quite vigorous, with firm pressure applied to each point for only three to five seconds. In contrast, in Jin Shin, the practitioner gently holds two points simultaneously for a minute or more.
Tuina Chinese massage also incorporates the use of acupoints, along with other massage techniques.
For pregnant women, studies suggest that maternity acupressure can relieve some of the unpleasant symptoms of pregnancy and reduce pain during labor. (Note that some points shouldn't be pressed during pregnancy because they may initiate early labor.) Here's a video showing how to find maternity acupressure points: