Another reason for the kihap/kiai is for focus... but not the kind that we have been talking about.
Think about a basket ball player, that can drain free throws all day in practice, when he gets to the line in game, he chokes. One of the reasons is the difference between our conscious mind and our subconscious mind. In practice, he was counting the shots, talking to his buddy, wondering how much longer, thinking about what he was doing after... basically, everything but the shot. Meaning, his shot was being done with his subconscious mind. So, all those repetitions, were done by the subconscious, not the conscious mind. Now, when he gets to the real game, he wants to use his conscious mind to make the shot, so he focuses on the shot. He is taking the shot, in the way that he has the least amount of practice.
This is one of the reasons that shooters are taught to look at the front site when shooting. It gives their conscious mind something to do, while the subconscious mind does the shooting part. Remember, its the subconscious mind that did most of the shooting reps.
So, when training, we are usually thinking about other things. (when will this stop? did anyone see that last one? when can I ask my question?...) Our technique is done subconsciously. Part of that is taught as a kihap/kiai. When you need to do it for real, your conscious mind can focus on the yelling bit, while your subconscious does the rest of the important bits.
You would never have a student break a board, unless you knew they could. They don't yell, and fail, because their mindset is wrong. They are worried, and they are letting their conscious mind interfere with the technique. When you get them to kihap/kiai, they focus their conscious mind on that yell... thus staying out of the way of the subconscious mind, that actually knows what it is doing. Now, suddenly, the board breaks due to the awesome power of the yell... or more realistically, due to the awesome distraction to the conscious mind the yelling caused, which allowed the subconscious to control rest of the body to its full potential, with out having to fight for control.