I think our natural tendency is to hold our breath when performing an action, but that's actually a physically taxing - even weak - move. When you breath in, and then hold a breath, you use muscles to do it. It takes power away from the body, from the actions. Breathing out, however, does not. It takes no power. We breath out when cutting/striking, because we can put more force behind it. Breathing out is an action of power.
It's also a part of why so many parts of the waza end together. Wasted motion is, well, wasted motion. Stepping, strike, and exhale at the same time. Step back, end chuburi, and exhale at the same time.
One time I stumbled and lost my balance in class because I didn't realise I'd been holding my breath that tightly or much. I got dizzy.
Tension in the body also takes away from your power, including locking your knees. You can't put force behind a cut if you're too tense, because you've used all your force, and there's no give when you move. I think ballet is the only thing in the world where locking of the knees is desirous. It actually makes you terribly unstable in iai (and other things), to lock the knees.