The seemingly miraculous ability to walk on hot burning coals without being burnt is used as a religious ritual in India and in many new-age quasi-religious groups as a rite-of-passage or as a faith test, and by life-coaches as a way of showing how you can 'overcome the impossible'. But it can go wrong. In 2012, San Jose firefighters treated 21 people for burns when they walked across hot coals at an event by motivational speaker Tony Robbins.
It's believed that fire-walking began in India and has been documented for at least 3000 years. As a modern phenomena it became a tourist attraction on the islands of Fiji about 120 years ago and eventually spread to the west in the 1970's, being picked up by modern life-coaches and new-age gurus. It is frequently held to imply that the feat requires the aid of a supernatural force, strong faith, or on an individual's ability to focus on "mind over matter" and nowadays it is often used in corporate and team-building seminars and self-help workshops as a confidence-building exercise
The science is fairly well understood and depends on the temperature of the coals (500/700 oC) and the length of the walk (4-8m). Various additional effects help stop burning; embers have a very low specific heat capacity, which means they do not lose heat very well, whereas water does, so your temperature of your feet stays more stable. As your feet sweat, a layer of liquid insulates them from the heat and as long as you keep moving at a regular pace (not too fast or your foot may sink into the coals) and not for too long, you will remain unburnt. They may be damaged however, if you walk too long, the coals are too hot, the embers contain foreign objects (especially metal) or the embers have not burnt long enough to evaporate any moisture in them.