Ireru means "to enter", whereas
mawaru means "to turn/spin around".
We say
koshi-o ireru: "to put your hips in" or "cut from the hips." What most people tend to do is just turn their hips instead of put them "in". I usually describe it as snapping the whip: cock your arms above your head, step out with the rigth foot, then spring the upper body forward and finally, like the crack of a whip, swing your arms and the sword. The blade itself is probably moving nice and fast, but the timing is all off. Once you've stepped your foot forward you are in the kill-zone: you can reach your enemy, and so he can reach you. If you stand there with your arms above your head as you crack that whip, by the time you bring your sword anywhere near him, you've already got his sword buried in your throat.
When you step into the kill zone, the sword must move in as well so that just as you step in your sword is just about into his head. To do this, the hips drive the shoulders, the upper and lower body moves as one. No whip-cracking, no twisting and unwinding; everything has to move as one, centered from the hips. It might initially feel as powerful as a nice big spin and unwind, what with all the centrifugal force, but your sword will go where it needs to go and get there in time. And more importantly, once the hips stop moving, so does the sword, so that you can finish the cut with the sword pointing at the enemy, not off someplace else. Very important in the obvious case that your first cut doesn't finish things.
I've mentioned before that in Japanese
hayai means both fast as in speed, and fast as in time. Most people focus on the speed of their own movement in a vacuum, but speed is useless without proper distance and timing to the other guy who is also trying to kill you with his sword.
The fastest, strongest cut in the world is no good if it's a tenth of second
after you've taken 20 centimeters of sharp steel into your skull.