The runner's high is a state of euphoria that is experienced by not only runners, but by anyone engaged in a vigorous workout. Boxers and bikers have reported similar states of being, as have weight lifters, cross country skiers and rugby players.
The high itself is variously described as a feeling of well-being, to being one with the world or to a total out of body experience. It is typically related to longer periods of vigorous exercise rather than shorter, easier workouts, possibly due to the stress the body undergoes as the major muscle groups begin to run short on glucose. The experience of the high also seems to rely on the individual makeup of the runners themselves, with some experiencing it at 5 miles, while others must run 20 before the euphoric feelings kick in.
The exact mechanisms underlying the runner's high have been debated for years. Endorphins, the natural opiates of the brain, were assumed to be the basis for the good feelings associated with the runner's high, but a variety of other chemicals have been put forth as a possible cause.
This debate has seemingly been brought to an end by the results of a 2008 German study of long distance runners. The study showed that not only did periods of robust exercise produce endorphins, but that the degree of euphoria reported by the runners correlated to a surprising degree with the endorphin levels seen in their brains. In essence, the study found that the higher the endorphin levels, the greater the degree of euphoria experienced.
The runner's high is an extreme intense feeling, and like all such, can be habit forming. "Exercise addiction" is a rare but real condition thought to be caused by an addiction to the endorphins produced by the runner's high. It's typically characterized by an OCD-like compulsion to exercise to the exclusion of all other activities. So run, and run well, but run for yourself, or for your health or to compete, and let the high be a happy byproduct of that exercise, rather than the goal.