A lot of it is athleticism. Squats, split squats, box jumps, these will all do well.
Mechanically, it's like what I have in the chicken article, you need to be BIG on the kick, you come up on the ball of the foot and you lift yourself into it. Keep in mind that a lot of the time you won't necessarily feel the difference but your opponent will. If you're kicking from 12-6 you will usually just be tagging them. Normally the best thing to do is take a small step to the outside and drive the hip THROUGH the opponent. Similar to what one of the earlier posters said.
I personally prefer a narrow arc on the kick, where you kick upwards and turn in - this is typically how Thai's kick (the arcing round kick you're taught in thai classes in the west isn't really indicative of traditional muay thai). When you kick in a wide arc, what happens is the kick comes out and round and by the time you've hit the target you're near the end of the movement.
With a narrow arc the kick will come upwards and in and you hit the target as you're accelerating rather than on the end. Keep in mind that striking power comes from the acceleration, not the speed itself.
http://8limbs.us/muay-thai-thailand/golden-kick-how-to-improve-your-thai-kick < this goes into it quite well. It's portrayed a little bit as a forgotten technique in this article, and I don't really think that is the case, but either way it's good to explain how to make your kick more reliable. This is pretty much how Yodsanklai kicks most of the time.