Kokyu ("呼吸") is a much used word in Aikido. Not only does the term occur in one of the fundamental throws, Kokyu-nage, but it is also used in the exercise, Kokyu-dosa (which, by tradition, should be practised at the end of every Aikido session) and Kokyu-ho (various exercises often involving movement while being held).
Kokyu is the Japanese word for ‘breath’ and many books translate ‘Kokyu-nage’ as ‘the breath throw’ – which seems to suggest that you should be doing some pretty nifty breathing while throwing. It is certainly the case that some people may find ‘kokyu’ exercises, such as kokyu-dosa, easier to do if they breathe in harmony with the technique. Even so, I have to admit that I have never really felt that kokyu-nage involves more or less ‘breath power’ than any other aikido throw.
In Koichi Tohei’s classic book "Aikido, The Co-ordination of Mind and Body for Self-Defence", Kokyu is defined as “movement of your Ki or the movement of your body following Ki.” Tohei says that “The arts of Aikido are concerned not only with physical matters but also with Ki, Kokyu Ho is the way that leads others by Kokyu, and Kokyu Nage is the art of throwing others by Kokyu.”
The one thing you may notice in this description is the complete absence of the word “breath”!
Gozo Shioda, founder of the Yoshinkan school of Aikido describes kokyu power as “focused power” (you can read a free sample chapter on Kokyu from Shioda’s book, ‘Aikido Shugyo: Harmony In Confrontation’ here: http://www.shindokanbooks.com/shugyo.shtml).
To help clarify this confusion, I asked a Japanese friend for some assistance in making sense of the Japanese meaning of the word, kokyu. She tells me that “Kokyu” has four main meanings, the first of which is, indeed, ‘breath’. But it can also mean ‘an art or knack’, ‘the gist of something’ or a ‘rhythm, tone or tune’ and that it may suggest a sense of harmony.
Thinking of kokyu-nage as a throw that uses ‘focused power’ or harmony with Ki makes much more sense to me than its rather prosaically literal translation of ‘breath throw’. This is, after all, what we try to do throughout our practice of Aikido.