Acupressure is an ancient Chinese technique based on the principles of acupuncture, and involves the use of finger pressure (without the needles) on specific points, so called acupoints, along the body. The term "pressure" is misleading, since acupressure actually uses a very light touch.
The purpose of acupressure is to stimulate the body's own recuperative powers by stimulating the various points. According to Traditional Chinese Medicine, the qi (the lifeforce energy) travels along the meridians. The stimulation removes energy blockages by diffusing the toxic build up that accumulates and therefore causes all sorts of complaints.
It IS a science, and there is nothing supernatural or magical about acupressure. Western scientists have proven the existence of acupoints using electrical devices.