Kang & Yu are very important concepts in every martial skills. Here, Kang and Yu refer to opposite items to each other, which, however, can be pararell together. The original meanings of Kang and Yu can be said of hardness and softness respectively. But Kang also implies the "power" or "powerfulness" while Yu also implies the "obedience".
The pair of Kang-Yu is to be controled and can be united in one along the Samjae. If you can understand the logical structure of Samjae and Kang-Yu, you will be able to use almost kinds of skills as you want.
In Taekwondo skills, the essence of Kang is "concentration". A weak power can break into a strong opponent's defense or resistence by way of concentration, as a nife with a sharp edge can stab a soft material easily. The sounds of "Kang" and "Con" of concentration are similar by chance, which is interesting. By way of concentration you can surpass your opponent since you concentrate your whole on a small part of his, and big power can surpass small resistence with ease.
The essence of Yu is "following you". It refers to the obedience. Along Yu you have to follow what your opponent(He is you to you who are I) with no resistence. This is what Yu means in skills. It can be understood as to make use of the opponent's power in the attack at him. Obeying his motion you can ride it to re-use it for attacks at him. Your force is very soft to him as a soft leave can be moved by a slght wind.
The figure of Kang is breaking into his resistence. The figure of Yu is moving together with him. When you say "When you hit your opponent you should break his will with yours, oppress his tide down with your tide, scatter his vigor with your Ki-Hap and hit his trunk off with your weapon. When you block your opponent's attack, you should empty yourself to lead his intention in vain, carry your tide on his and scatter his sharpness rather absorbing yourself in it to make your attack. Why are they not same?(Chapter 38 of PPT)" you are talking of Kang-Yu.
The reasoonable aspect of Kang & Yu can be said to be effect way of getting control over the opponent. And it is what we want to get in whatever martial art. More detailed explanation will be provided in "On Samjae & KangYu". But let me notice it will really much time to build up that site. Perhaps several years.