The kata of kendo are a series of movements developed from the fighting techniques taught and used by skilled teachers in the past. As such they maintain a direct link with classical swordsmanship and are essential in the further development of the fundamental skills developed through shinai kendo.
There are many different kata sequences, each being developed through the particular style of the original teacher, and between 1886 until around 1912 moves were made to produce a standardised kata form in kendo. This established the Nihon Kendo Kata which is still used in the grading assessment of all kendoka.
Recently a second kata form has been introduced by the AJKF, the Bokoto ni yoru kendo kihon-waza keiko-ho. This kata reflects the techniques and movements made during shinai kendo and, whilst initially aimed at teaching beginners, it contains important skills applicable to all levels of practicing kendo.
For more information about Bokuto-no-kata please follow this link to Steve Plimbleys report from the visit of Nagao sensei.
For more information about Nihon Kendo Kata please see "Looking at a Far Mountain" by Paul Budden, an excellent english sourcebook for the subject.