This idiom is used to describe heavy rain. Example:
It was really raining cats and dogs yesterday! (It was raining really heavily yesterday!)The image of cats and dogs falling from the sky seems so incredibly ridiculous and crazy. That's how I used to explain the origin of this idiom, but yea, I didn't really know anything.
A book I read claims that the origin of the idiom came from 17th century Europe. Then, the drainage systems were inadequate, so after a heavy rainstorm, there would be dead cats and dogs littering the streets. This is cited in Wikipedia as well.
Enjoy, try to use this when it rains heavily in your area next time.