Well, you're half-way there. It's pure physics, actually.
Since impact force is positevely proportional to mass and velocity, in order to hit harder you need to:
1. Gain mass. With proper technique you can put much of your body into the blow, not just the striking limb. You can further improve on this by weight training, which is commonplace among Kyokushin practitioners.
2. Increase velocity. Fists and feet can travel faster when respective muscles in your arms and legs are relaxed rather than tensed.
Well, I didn't want to mean that I don't actually understand what he's saying, it's rather that I'm curious about much of it being substantially different from my style's way of doing things. His style seems to be very soft in general, not only when actually hitting stuff.
Do you happen to know something about his Karate background?