First off don't buy this game for the story or anything like that, because after playing it it's all still a big WTF to me.
Bayonetta is a member of a clan of witches who were in an eternal battle against the angels, the witches gained the upper hand and the humans saw how powerful they were becoming and held the witch trails killing off the majority of them.
Now I'm going to start my complaints about the story. How on earth did humans kill these witches with all the magic and abilities they possess? And they talk about how the world of Inferno (Hell) and Paradisio (Heaven) Purgitorio (Purgatory) are interacting too often with the human world recently, but they were feuding back in Renaissance Europe.
Getting back to the story. After the introduction you pick up where the demo kicks off, and basically Bayonetta decides to go fight stronger angels, and on a quest to find a jewel in the hope of gaining her memory back. And that's the story without any spoilers (as always).
The gameplay of Bayonetta is where it shines. Every aspect of the gameplay is near perfection. Each weapon you equip to Bayonetta give you a diverse and new way to play, and all the powers Bayonetta has make her feel so powerful against your foes. Mixing items together and stirring them as if the were a cauldron was brilliant. Bayonetta is a true hack and slash dream come true in the gameplay department. Boss battle are very cinematic and challenging, and the game is just a bliss to play. The only damper is a slow camera. The for some reason moves slower than a grandma with a walker, but thankfully by pushing in the right stick it resets to the direction Bayonetta is looking. Loading screens are good and bad. Good because they let you practice combat, but they are a bit to frequent (and that's on the Xbox 360 so PS3 owners I feel sorry for you). You have to get use to dodge a lot, since you'll be needing witch time especially on the harder difficulties.
The music in the game is forgettable, unless you like elevator Jazz music or Japan pop. The voice acting is sub par with the exception of Bayonetta, and the dialog is god awful "How do the Americans put it. Ah yes, bust a cap, in yo ass" (Bayonetta).
Overall Bayonetta is one of the weirdest, and probably the most awful written games I've ever played, but there's no denying that the gameplay that's here is among the best of the best.