Meaning
Raining very heavily.
Origin
Raining cats and dogs 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.
Rainbow?