The reason I do kayaking is not because I think it's beneficial to parkour. I do it because it's an enjoyable activity- I enjoy it in the same way I enjoy parkour; I enjoy the sense of continual improvement, the learning, the thrill from moving through the rapids, the feeling of achievement when I successfully get from A to B on a river, putting my strokes into practise in order to do so, and recovering from any difficulties such as being tipped over and being able to roll back up safely. I didn't realise until recently how similar my attitude to kayaking is to my attitude to parkour. Some people like doing tricks and what's known as "freestyle" - I have a dabble in that to see if I can do it, and do enjoy dabbling, but my main interest lies in running rivers and putting useful challenges upon myself. It makes me feel great - much the way parkour does. The only difference is that parkour is all-round where as kayaking is just water; rivers, lakes, seas, etc.
Ok here's a sort of media-friendly definition I put together a year or so ago for my website:
Parkour is a French discipline, a training method devised by David Belle, inspired by his father Raymond Belle, and Georges Hébert, a French physical educator, theorist and instructor who lived by and taught the ways of la Methode Naturalle or the Natural Method.
Parkour is the art of movement, the aim of the activity is to move through any environment as quickly and efficiently as possible using principally the abilities of the human body. Practitioners of parkour are recognized as traceurs. It should be noted that Parkour is non-competitive and is purely a programme of self-improvement rather than a basis of comparing skill level with others.
I have been practising parkour since January 2005 and since a year or so into training it has become an integral benefactor to my healthy lifestyle; it has made me think about how I treat my body by the things I eat and drink, and the way I train to prepare myself for continual improvement and accompishments in the physical side of parkour. I also love the opportunity to spread the word of parkour by helping others get involved and answering their questions.
(The last paragraph is more personal to what parkour is to me)