A recent entry on Platinum Games' blog explains exactly what effects are by showing us what Bayonetta looks like without them. For those who'd rather hear an explanation of all these visual flourishes using the clunky, unfitting art of language, effects are generally things like fire, smoke, and whatnot. Without them, Bayonetta looks kinda weird.
The movies are only a few seconds long each, though, so why not check them out? Both are after the break.