I found an answer to your question in a book called, "Why Moths Hate Thomas Edison and Other Urgent Inquiries into the Odd Nature of Nature," edited by Hampton Sides:

"Variations of this ancient saying turn up in Shakespeare and even in the Gospel of Matthew. Some meteorologists have estimated that the 'night' part of the proverb can be as much as 70 percent accurate in forecasting rain--not bad, as folk wisdom goes, but not good enough to drive the Weather Channel off the air.

There's no consensus on why it works as well as it does, but here's the basic concept: Sunlight comes to us through more miles of atmosphere at dawn and dusk than at other times of day. When the sky is clear, the atmosphere scatters the light at the blue end of the spectrum, leaving mostly red. But if the light passes through larger particles, such as water droplets, you tend to get paler light. A ruddy sky at sunset, then, can indicate that there is little moisture in the upper atmosphere west of you, where tomorrow's weather generally comes from--and thus sunny skies are in the forecast. It might also be a situation, say some meteorologists, in which the setting sun in simply reflecting off the underside of clouds on the eastern horizon, which suggests that rainy weather has already moved beyond you.

The second part of the proverb is the subject of endless speculation among professional meteorologists. More importantly, it isn't the least bit reliable. So when morning comes, sailor, don't even bother looking for red in the sky: you'd do just as well to flip a coin."