Imagine a day when it rained. What happened before that? Maybe you heard thunder, or, most likely you saw the sky and said, "It's dark. It's going to rain. I am a genius."
Well, that doesn't happen in Minecraft. You're happily enjoying punching wood under a clear sky, and, all of a sudden, BOOM! It starts raining.
I think that a few minutes before it starts raining, the sky gradually darkens. In the time it takes to reach light level 12 (or whatever it reduces the light level to), there is a random chance that it'll start raining. For thunderstorms, you will hear distant thunder, and as it gets closer, the sky darkens.