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 could be grasped by imagining a race through an obstacle course, the goal is to overcome obstacles quickly and efficiently, without using extraneous movement. Apply this line of thought to an urban environment, or even a run through the woods, 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. If the intention is to get somewhere using the most effective movements with the least loss of momentum, then it could probably be considered Parkour.
What isn't Parkour?
Parkour is not acrobatics, tricking, stunts, recklessness, or jumping off high objects for no reason. It is not any movement or activity that doesn't fit in the above description "What Parkour Is". It is also not "What you make of it" ... it is predefined and has a purpose, if something doesn't suit that purpose, it is not Parkour.
What is Free Running?
Free running was meant to start out an anglicized term for Parkour. It was first suggested to Sebastien Foucan during the filming of Jump London. Free Running has grown to be descriptive of a sort of "cousin" activity to Parkour - Free Running is more expressive and creative in nature, with moves such as acrobatics, flips, and spins added for flair, creativity, or just because someone wants to. The main difference then between Parkour and Free Running is that Parkour is defined by purpose "get somewhere quickly and efficiently using the human body", and Free Running is defined by the activity or art of moving through your environment however you want, moving your way, following your own path.