On the surface it looks like two people beating each other on the head with sticks. Kendo (or the Way of the Sword) is in fact a Japanese Martial Arts form practiced worldwide. It is essentially a form of fencing whose roots derive from the Samurai in Japan. Kendo's modern appearance first began in the 1700s with the introduction of armor (bogu) and bamboo and wooden swords (shinai and bokken, respectively).  Kendo is now practiced  internationally by children as well as adults as old as 80 years old. 


In the modern age, sword fighting has little practical purpose against weapons like the pistol- so Kendo is really more of a form of self-improvement than a practical fighting form- or as the All Japan Kendo Federation (AJKF) puts it, Kendo is "the way of developing the person."

The concept of Kendo is to discipline the human character through the application of the principles of the Katana. The purpose of practicing Kendo is: To mold the mind and body, To cultivate a vigorous spirit, And through correct and rigid training, To strive for Improvement in the art of Kendo; To hold in esteem human courtesy and honor, To associate with others with sincerity, And to forever pursue the cultivation of oneself. Thus will one be able to love his country and society, To contribue to the development of culture, And to promote peace and prosperity among all people. Source: All Japan Kendo Federation

You can really only appreciate it by experiencing it- even if just by going to watch a practice or a tournament. Most dojos allow guests to watch practice sessions and many tournaments are open to the public.  For me, personally, besides being a great physical workout, Kendo teaches one to be decisive, precise, calm, humble, generous, courteous and respectful toward others. As a university professor, I find it a lot like going through graduate school again.  If I had taken Kendo when I was in graduate school I probably would have been a better student. But it's never too late to learn... It  seems like a contradiction in terms that one could learn all these qualities through what looks to be a "violent sport".  In fact, if you go to a Kendo tournament or practice, you will find the practitioners surprisingly courteous and welcoming. 

For an inspiring documentary on the subject check this link out (it's 85M in size so be patient).
For more introductory info on Kendo visit the All US Kendo Federation web site.