Do any know the correct translation for Hidari? I think it means left side. As in Hidari Kesa Giri meaning left side downward cut. Is this correct? Thanks.
Kesagiri does not translate to 'downward cut' though. It is generally a diagonal cut following the line of the keikogi.
Odds are it means "left" as in "left side", but you can't be entirely sure unless you see the written form. Japanese has a large number of homophones due to its limited number of phonemes.
Kesa (袈裟) is the Japanese name for the robes worn by Buddhist monks. As ScottUK pointed out, the name implies the contour of the robes (or keikogi) from the shoulder to the opposite hip. http://en.wikipedia.org/wiki/Kasaya_(clothing) Some styles also use kesagiri to denote cutting from the hip upward to the opposite shoulder.