Parkour is the art of moving through your environment using only your body and the surroundings to propel yourself. It can include running, jumping, climbing, even crawling, if that is the most suitable movement for the situation. Parkour can be grasped by imagining a race through an obstacle course. The goal of parkour is to overcome obstacles quickly and efficiently, without using extraneous movement. Apply this line of thought to any type of environment, whether it is urban or natural , and you're on the right path. Because individual movements could vary so greatly by the situation, it is better to consider Parkour as defined by the intention instead of the movements themselves.
Parkour is not acrobatics, tricking, stunts, recklessness, rebellious, or jumping off high objects for no reason. If the movement does not help you effectively overcome any type of obstacle, it is not parkour. Parkour is also not what you make of it; it is predefined activity.
Many people take the principles they learn through parkour and apply them to their lives. By challenging themselves physically, it becomes easier to deal with everyday life situations. When an obstacle or difficult situation comes up in daily life, a Traceur (parkour practitioner) can see this as just another obstacle to overcome quickly, efficiently, and without disruption to the intended path. Update: After speaking with David Belle, I feel it should be added that part of the overall Parkour philosophy is to be useful in a variety of situations. Parkour itself does not strive to be a "complete" discipline.
While the concept of Parkour cannot be grasped by looking at the individual movements, it is necessary to drill some basic movements to attain a level of proficiency in Parkour. There are some basic techniques that should be mastered in order to ensure one's safety and success in their parkour journey. To view tutorials of some of these basic movements, please click here.
In some sense, Parkour has been around as long as man's need to hunt and avoid being hunted. Humans naturally have an astounding range of motion and range of options for how to move through a given set of obstacles. Furthermore, children naturally move about with grace and ease. We only start to lose this ability later in life as we start to move with conscience. There have been several people throughout history to work on concepts of human movement and development. The man who inspired parkour is Raymond Belle, a French soldier in the Vietnam war. He and his companions worked to develop efficient methods "to reach or escape". These were then handed down to his son, David Belle, who has spent a majority of his young life working on these principles specifically as Parkour. There were some others who worked with him in the developing stages of Parkour in Lisses, Sebastien Foucan being one of the most well known.
*Information courtesy of American Parkour.