Someone at work asked me what this phrase meant the other day. I just got around to looking it up. It refers to the weather condition when it is sunny but raining. I never knew there was a term for it. I always just thought of it as "Hawaii weather." Apparently, the following phrases also mean the same thing:

"foxes are on a marriage parade"
"witches are doing their wash"
"a tailor is going to hell"
(source)

To these, I would add another:
"The Big Monkey in the Sky Is Peeing on Us, Violently"

Mine makes a hell of a lot more sense than that foxes' marriage parade bullshit. Fucking illogical weather arcana!

UPDATE: Duh, I completely forgot the term "sunshowers."