For those of you who haven't played Bayonetta but might be interested in this:
Imagine a simple action game which has combos (like DMC, or GoW, or NG - whichever). Let's take a simple combo like punch --> kick --> punch.
In some games, you have to press PKP in quick succession to deliver the combo. Let's bring this up a notch, and allow the player to hold down a button to delay the combo delivery. So, punch --> kick --> hoooooold --> punch. This flexibility in timing is nice, allows you to not jump right into the enemy attack or something, or to time your combo to hit just before the enemy's own attack. Nice, but simple.
Now, let's attach some weapons to your arms and legs. Let's say, automatic pistols. So you can punch and kick, but whenever you hold one a P or a K, your pistols will keep shooting at the enemy. This allows you to continuously stay on the offensive even when you're stalling an attack/combo.
Don't you hate it when some games don't allow you to cancel attacks? Say, if you commit to a combo, you can't back out of it, even if you realize you screwed up and are going to get hit. Let's add a simple design element - you can dodge/cancel any attack, whenever. Cool, huh? So, you can PKP, or PKhooooooldP, or PKdodge --> combo cancelled.
Okay, let's add in the master design element. Let's say you can resume your combo after dodging. PKhooooooldDODGE-->P = finish combo. So not only do you hold control of the timing of the control, not only do you continue maintaining an offensive (via rain of bullets while holding or dodging) throughout, not only can you dodge during a combo, but you can resume your combo right where you left it off. I just blew your minds.
Oh wait, there's one last crucial element I forgot to mention. You can bypass steps in the combo by timing an attack at the same time as a dodge. So, if you dodge RIGHT as you're punching or kicking, they get added up to the combo, without needing to punch or kick. So, dodge(P) --> dodge(K) --> unleash final P move from the combo = giant magic fist, without actually having gone through the early steps of the combo.
Imagine the implications during combat. You're fighting a big baddie. He strikes at you, you dodge. You dodge through the second phase of his attack as well. You've now landed behind him, get in 2 punches. By then, a smaller enemy has approached and jumps at you, you dodge that as well, and unleash the finisher move of a 6-move combo at both of the enemies at the same time. You might have pulled off a complex PPPPKK combo dynamically in the middle of a fight. With a reactive enemy, a 6-move combo can be very hard to pull off. If you're pulling it off while dodging and skipping steps (eg. while you're fighting), it becomes a reality.
That is the essence of Bayonetta's genius. It is, of course, barely scratching the surface.