The noun parkour designates the discipline of moving rapidly and freely over or around the obstacles presented by an urban environment by running, jumping, climbing, etc.

The nouns parkour and free running are frequently taken to be synonymous, although in some usage the two are differentiated, with parkour emphasising the importance of efficiency and fluidity of movement, while free running places more emphasis on acrobatic techniques, performance and self-expression.

In Why parkour is a cure for the fear of being human, published in The Guardian (London and Manchester, England) of Wednesday 1^st October 2014, Mary Hamilton, who was training at the Australian Academy of Parkour, Exercise and Self Defence (Aapes), differentiated the two disciplines as follows—the noun traceur designates a participant in the activity of parkour:

Parkour—as distinct from free running, which is much more of an expressive discipline—is not about flips and tricks, or being able to pull off impressive feats of gymnastics on the streets. At its core is a philosophy of self-improvement that validates individual progress above everything, and acknowledges that something that feels ridiculously easy to one person might be incredibly hard to another.
Fear is as much of a blocker to most traceurs than physical ability. Actually jumping off something tall takes not just strength and technique but also mental discipline: you have to be willing to face your fears and commit to movements, trusting your body’s ability to take you where you want to go.

Of French origin, parkour is an altered spelling of the noun parcours in parcours d’obstacles, translating as obstacle course.

It seems that it was a Frenchman, David Belle (born 1973), who coined the noun parkour to designate the discipline he invented.

The earliest occurrence of the noun parkour that I have found is from No ropes or safety net for BBC’s Spiderman, by Alex Benady, published in the Evening Standard (London, England) of Thursday 18^th April 2002 [page 3, columns 3 & 4]—Tom Ewart was an employee of Abbott Mead Vickers, the advertising agency which made the promotional film:

TV viewers this week have been spellbound by a new BBC1 promo showing real-life Spiderman, 28-year-old French athlete David Belle, performing a series of stomach-churning stunts over the rooftops of a busy city.
[…] It is the first on-air promotional film for the BBC’s flagship channel.
Although there are no identifiable landmarks, it was shot in London over seven days last month. It shows a man leaving work through his office window and crossing the gridlocked city by leaping over rooftops to get home in time to watch his favourite programme on BBC1.
[…]
The rooftop surfing, however, is part of a new form of urban martial arts currently taking France by storm. Called Le Parkour—the obstacle course—it is a mixture of acrobatics and daredevil antics developed by martial arts expert Belle. Obviously, concentration and grace of movement are crucial. Ross Kirkman, who worked on the shoot, said: “These aren’t stunts, they are moves. The shape of the body and the way the arms are held during the leap are absolutely vital.”
Belle is currently on retreat in Thailand. He developed his new sport after moving to Paris from the Normandy countryside when he was 10.
Mr Ewart said: “He loved climbing and jumping in the woods. But when he got to the Evry housing estate in Paris, he suffered real culture shock. So he simply transferred what he had been doing in the country to the town.”
He was encouraged in his new hobby by his father, an orphan who had been brought up by the army in Vietnam, which friends say explains Belle’s intense self-discipline and interest in the Orient. Le Parkour has made Belle a hero in France and looks set to do the same here. In 14 years, he claims never to have had an accident. But don’t try this chez toi.