As the name states, it is the act of relaxing your muscles, body part by body part, until the whole body is in a state of total relaxation. It is done differently person to person, culture to culture, as are the reasons for doing so. Myself? I usually use this technique when I am trying to sleep, or when I am getting stressed out at school. But heaven forbid I use it at work.
The usual approach I take is to shut my eyes, get myself into a comfortable position, then the process begins. I relax my toes, then the rest of my foot, then my shin, knee, thigh, pelvic girdle, fingers, hands and wrists, forearms, elbows and upper arms, lower torso, upper torso, neck and head, at about fifteen to twenty second intervals. I never have music playing, but it is always good to, since it helps the relaxation process. Then, usually I imagine myself in calming situations. If I'm still awake after a 20-minute session, I have basically done it wrong, or I am too excited by something to sleep.