The ordinary telegraph is like a very long cat: pull the tail in New York, and it meows in Los Angeles.
-- Albert Einstein
Einstein's genius is that he compared the telegraph to the cat -- the temptation, especially for someone who knows a lot of science, is to do the opposite, to say something like, "The nervous system of a cat is rather like a telegraph: in the tail, physical motion is encoded by nerve fibers into a set of electrical signals that flies up the spinal chord and into the brain, where it is decoded back into physical motion, in the form of neurotransmitters flowing between the neurons, and into other electrical signals, which jump down the axons and create the sensation of a tug."
It's a good explanation -- precise and accurate, fairly interesting, conveying relevent information, but it doesn't impart any sort of intuitive feel for what's going on, and it's not the sort of thing you'd tell a 10-year-old.
We know what cats are like; we've interacted with them for years, since childhood -- when confronted with the idea that telegraphs and cats work on the same principle, it's much more useful, in most contexts, to think of the telegraph as a strange sort of cat than the other way around.
Essentially, the other writeups in this node are saying, "the sky is blue because light waves of blue length are reflected in all directions by the atmosphere, while other wavelengths travel straight from sun to eye and are seen as originating from there, not from elsewhere in the sky."* A good answer, but not really a satisfying one, and probably not what most people who ask the question are looking for; in a way, it misses the point:
The sky is blue because air is blue.
Of course, most people think air is clear -- and it is, mostly, but it's clear in the same way the water of a swimming pool is clear: which is to say, it's not entirely clear, it's translucent. The Earth's atmosphere is a very, very light blue, a blue that only becomes visible when you're looking through miles and miles and miles of it. As they say in art class, when teaching perspective drawing: "Farther objects should be smaller, hazier, and bluer." Bluer, because the air makes them blue, like the the wall of a swimming pool looks green through the chlorinated haze, like a figure emerging from fog looks white.
* This is a simplification, of course, but not an oversimplification. Yes, there are situations in which the atmosphere scatters light to your eyes of other wavelengths, and for a full understanding of the way it all works it helps to know the technical details -- but the same can be said for any object. A blue couch doesn't look blue when illuminated by orange light; your hand looks red when a flashlight beam is shone through it; the back of a white billboard is brown.