Something happens quickly if it happens in a very short space of time, or after a very short delay. Quick might also be another word for fast. The opposite of quick is slow.
The squirrel in the picture is running very quickly.
Something is quiet if it doesn't make very much noise. Somewhere is quiet if you can't hear much noise when you are there.
The opposite of quiet is loud and if there is no noise at all, it is silent.
