Biofeedback is the technique, but there are many kinds of different approaches to biofeedback, self monitoring, and self control of your body's systems and functions. Most of the body's internal functions were thought to be autonomous (meaning that we had no control over them in any capacity except through exercise and outside influences - not direct mental control). As it turns out, using biofeedback devices can train you to control your body's heart rate, your muscle tension, your gastrointestinal tract, your blood pressure, and your responses to stress. The training involves being monitored in real time, and the most common of course is EMG monitoring of muscle tension. As you watch the results you can actually correlate what you feel to them, and eventually you learn to control them (much like riding a bike or learning to balance well after much trial and work). Eventually you get to the point that you can have complete control over your body's muscular systems.
Thermal biofeedback lets you see your body's skin temperature and control your stress through seeing your responses to it - the less stress you have and the more you are able to keep it from effecting you is likely to help with blood pressure and in turn help in controlling your circulatory system - keeping it from developing unhealthily with high blood pressure that puts you at risk for heart disease and other physiological problems. Finally, there is Neuro-feedback - aka EEG, which measures the brain waves and the brains activity.
In a normal session with any and all of these forms electrodes or sensors are attached to the skin - these then send information to a monitoring device that translates the information into a tone that varies, or an on scree display. It all depends on what you use and what you see, through practice people will learn to control and identify the mental activities that will bring about the desired physical and physiological changes.