There are many good descriptions of what kendo is and its history already in existence out in the world wide web so rather than duplicating them this page will link to a few of these other sites.
“Kendo (剣道 kendō?), meaning “Way of The Sword”, is a modern Japanese martial art of sword-fighting based on traditional samurai swordsmanship, or kenjutsu. Kendo is a physically and mentally challenging activity that combines strong martial arts values with sport-like physical elements” – http://en.wikipedia.org/wiki/Kendo
Brief History of Kendo written by the International Kendo Federation
Kendo Part 1
Kendo Part 2