Kiai means spirit shout. If you do it right then you will be using your diaghram. There are many reasons to kiai and it is an important part of the art. Also, it takes years of practice to do it right as I'm beginning to find out.
Kiai as uke when hitting the ground so that you do not get hurt. You will tend to be more stiff without a kiai and you will probably get the wind knocked out of you at the least. A kiai will not allow you the chance to hold your breath, which we all do but don't think we are doing. Kiai in attacking to stun or pause your opponent. Kiai to rid yourself of fear. People that do a silent kiai are generally just embarrased about shouting. Thalib knows what he is talking about though, and I doubt that he practices only silent kiai. My teacher once scared an attacker with his kiai so much so, that the man fell down. This would be pretty difficult to do silently.
If you want to know if you kiai correctly then stand about 5 feet away from a guitar. Kiai. If all 6 strings vibrate then you have a good kiai. I can only get 4 right now. As is said below, there should be no stress to the throat. The technique is the same that opera singers use and some of them have the ability to break glass with their voices. I will say at the very least you should kiai everytime you are thrown so that you remain safe.
Originally posted by Thalib
Karaa-san, when one needs a vocal incentive in order to reach kiai, one just does not shout from top of their lungs and through their throat. This will be very exhausting and one could get a very sore throat.
The voice should be coming from the hara. Abdominal breathing if you must. By concentrating on the hara, one will eventually be concentrating on one point (seika no itten or seika tanden) - the first step in unifying mind and body. In a vocal kiai, the voice comes out as a side effect of flowing the air to the hara.
Wether it is a platoon leader or a batalyon commander giving out marching orders (like "forward march" or "right face") on the field, the shout never comes out of the lungs, but it comes from the abdomen. An order given in a right way will make the soldiers respond correctly in a unified way. This is a type of kiai. There are many correlations between "ki" and military discipline, but that is another discussion.
In conclusion, regarding the sore throat, one should not stress the throat in order for the air to come out, but let the air flow through the throat.