Our coach introduced the practice of kendo kata today. Kata (形) are predetermined sequences of movements performed in pairs using wooden swords.
Under the current kendo grading syllabus, there are ten official kata forms. We went through the first form (ipponme) today.
The best way to learn kata is to see it done properly and then practice it, so rather than write at length about it, my suggestion to you is to watch this video: http://youtu.be/XWzdIpayeFk. The kendoka use metal swords in the video, but obviously we only use wooden swords (bokken/bokuto) in the dojo.