Before the supposed sudden appearance of these animal types there were simple organisms. There doesn't seem to have been anything in between. I think this is where the 'sudden' comes in.
This is where you are wrong and the more fossils we uncover, the more wrong you get. So no, it is not sudden and it doesn't go against evolution. But you would know this as you would have read the link. Which outlines the fossil problem.
Many phrases should good and are coined.
Like the Big Bang, it was actually coined by someone opposed to the Big Bang theory and said as a put down at a talk. You need to read into it more, not just go by the title.