Taken on the whole, Bayonetta is one big unholy mess of a game. Parts of it are good, parts of it are not, and I'm going to attempt to make enough sense of the whole thing for you to decide whether or not the good parts appeal to you enough that you're willing to put up with the bad.
Let's start with Bayonetta herself. Bayonetta is a 'witch' whose sexy librarian/schoolmarm look combined with her exaggerated hip movements, constant gratuitous crotch shots, and flashes of skin all seemed designed to appeal to a concept of sensuality that is pretty much reserved to boys too young to buy this game on their own. Bayonetta's constant over-the-top gyrations look silly at best to any man who's ever had a mature relationship with a real-life woman and will have women spending more time rolling their eyes than looking at the screen. Don't get me wrong – I'm not being prudish. I don't think that there's anything wrong with a game designed for a mature audience being sexy, but in this case it's all simply silly.
As for Bayonetta's story, well, let's just say that calling it a 'story' is giving it way too much credit. From what I can make of it Bayonetta is a witch belonging to a special order aligned with hellish demons locked in a war with heaven's angels. Bayonetta jump glides on butterfly wings, flowers spring from her footsteps, she blows kisses to break down barriers, and does it all to a bouncy J-pop soundtrack. On the other hand, angels look like buzzards and keep all sorts of nasty beasts in their employ. Oh, and Bayonetta has amnesia, but that doesn't give her pause when it comes to slaying angels and collecting their halos to trade for trinkets like power-boosting lollipops that she can mouth lovingly while taking a break from flashing her crotch at the camera. And lastly, Bayonetta's hair does double-duty of making her skin-tight bodysuit and turning into an angel devouring demon when needed. That's about all I can glean from the painfully bad and nonsensical dialog and tortuous cutscenes that everyone outside of masochists and twelve year old boys hoping for nudity will want to skip past.