Raining very heavily. / Llover a cántaros o estar diluviando
This is an interesting phrase in that, although there's no definitive origin, there is a likely derivation. Before we get to that, let's get some of the fanciful proposed derivations out of the way.
The phrase isn't related to the well-known antipathy between dogs and cats, which is exemplified in the phrase 'fight like cat and dog'. Nor is the phrase in any sense literal, i.e. it doesn't record an incident where cats and dogs fell from the sky. Small creatures, of the size of frogs or fish, do occasionally get carried skywards in freak weather. Impromptu involuntary flight must also happen to dogs or cats from time to time, but there's no record of groups of them being scooped up in that way and causing this phrase to be coined. Not that we need to study English meteorological records for that - it's plainly implausible.
One supposed origin is that the phrase derives from mythology. Dogs and wolves were attendants to Odin, the god of storms, and sailors associated them with rain. Witches, who often took the form of their familiars - cats, are supposed to have ridden the wind. Well, some evidence would be nice. There doesn't appear to be any to support this notion.
It has also been suggested that cats and dogs were washed from roofs during heavy weather. This is a widely repeated tale. It got a new lease of life with the e-mail message "Life in the 1500s", which began circulating on the Internet in 1999. Here's the relevant part of that:
I'll describe their houses a little. You've heard of thatch roofs, well that's all they were. Thick straw, piled high, with no wood underneath. They were the only place for the little animals to get warm. So all the pets; dogs, cats and other small animals, mice, rats, bugs, all lived in the roof. When it rained it became slippery so sometimes the animals would slip and fall off the roof. Thus the saying, "it's raining cats and dogs."
This is nonsense of course. It hardly needs debunking but, lest there be any doubt, let's do that anyway. In order to believe this tale we would have to accept that dogs lived in thatched roofs, which, of course, they didn't. Even accepting that bizarre idea, for dogs to have slipped off when it rained they would have needed to be sitting on the outside of the thatch - hardly the place an animal would head for as shelter in bad weather.
Another suggestion is that 'raining cats and dogs' comes from a version of the French word 'catadoupe', meaning waterfall. Again, no evidence. If the phrase were just 'raining cats', or even if there also existed a French word 'dogadoupe', we might be going somewhere with this one. As there isn't, let's pass this by.
There's a similar phrase originating from the North of England - 'raining stair-rods'. No one has gone to the effort of speculating that this is from mythic reports of stairs being carried into the air in storms and falling on gullible peasants. It's just a rather expressive phrase giving a graphic impression of heavy rain - as is 'raining cats and dogs'.