It's time for some serious public service. I know why the sky is blue, and I (hopefully) can explain so that nearly anyone could understand. The short answer is, "The sky is blue because scattering goes as function of 1/(lambda^4) and the sun is green." The long answer can be found below.
First, A little info on the nature of light and waves. Visible light is part of the "Electromagnetic(EM) Spectrum (which includes radiowaves, microwaves, infrared, light, UV, X-ray, and gamma radiation) . An electromagnetic wave is tricky to visualize, so I'm not even going to have you try. The important thing to remember is that the size (wavelength) of the EM wave determine how it interacts with matter.
To explain this a little bit, imagine you're on a cruise ship in the middle of the ocean. There are waves hitting the ship all the time, but they don't effect the ship at all because they are too small. If there was a wave that was as big as the ship, then the ship would be in trouble, and everyone would notice. Now, conversely, if you're a fish a cruiseship-sized wave doesn't phase you a bit, your whole little world just rides along with it. A smaller wave, however, that is about as big as you will jostle you around and be very disorienting.
The same is largely true of EM waves, they interact the most with electrical components that are of a similar size to themselves. Radio waves (AM and FM) are huge, and they interact best with big antennae giving you good reception. Gamma rays are tiny and interact best with little components of DNA, giving you three legged frogs. The size of EM wave that gives us, say, green light, interacts well with specific cells inside our eyes. Red light interacts with different cells in our eyes, and blue light interacts with other different cells. This allows us to see in color. Bees, and some other insects, have cells in their eyes that interact with Ultraviolet waves allowing them to see 'colors' that just don't exist for us. This part is very important, the size of the light wave determines it color. Violet light has the smallest wavelength, and red light has the largest. The colors go in this order Red, Orange, Yellow, Green, Blue, Indigo, Violet, largest to smallest.
Now lets discuss scattering. Imagine you have a gun that shoots ping-pong balls in a rapid fire fashion. Now imagine you shoot this gun at the same point on a wall. All of the balls are going to bounce off in the same direction. That is called reflection. Now imagine you shoot the ping pong balls into a big bowl of frosting. They're all going to stick to the frosting. That is called absorption. Now imagine you fire the ping pong balls into a crowd of running people. The balls aren't going to be absorbed (like they did with the frosting), but they don't bounce off of the people uniformly(like they did with the wall) They're going to hit the people and bounce all over the place. This is called scattering.
When light passes through the dusty atmosphere it is like shooting the pingpong balls into a crowd of people. One ray of light will hit one particle of dust and bounce off in one direction while a second ray will hit another particle and go off in another direction. As the amount of dust increases the amount of scattering increases too. This part is really important, the smaller the light wave the greater the magnitude of the scattering. Firing ping pong balls into a crowd makes the ping pong balls go everywhere. Firing bowling balls into a crowd... well you get the idea.
The last important puzzle piece is the idea of white light. Doing the classic experiment with a prism one can see that white light is composed of all the colors traveling together, but it is just a little bit more subtle than that. Imagine you have a harp. You can pluck all of the strings together and make one loud and pretty sound. If you pluck all the strings, but pluck the ones in the middle the hardest you still end up with a similar sound, but as the sound fades you will hear the ones you plucked the hardest longer than then rest. White light is all of the colors together, and it still looks white even if there is more of one particular color.
Okay, now lets combine the pieces. White light comes towards earth from our sun. In the atmosphere there are bits of dust. The dust in our atmosphere is tiny, and scatters the smaller wavelenths (blue, indigo, violet) around. The larger wavelengths(red, orange, and yellow) pass straight through. The scattered light works it's way down to earth slowly from all directions, while the unscattered light seems to come straight at us from the sun. So when we look at the sky, we are seeing light from the sun that has been scattered by the atmosphere(the smaller wavelengths). When we look at the sun we see the light that came straight through(the larger wavelengths).
If this was all there is to it, then the sun would look red, and sky would be purple. The tricky thing is that the sun emits more green light than anything else. This means that there is more blue light, and yellow light coming towards us than red or purple light (red orange yellow green blue indigo violet). In the evenings when the sun is low on the horizon its light is travelling through more dust, so it looks more red, and the light coming at us from the sky looks more purple.
So, there you have it. That is why the sky is blue. I hope it makes sense. If it doesn't you are more than welcome to ask questions, and I will be happy to explain. You are more than welcome to use the short answer on your kids when they ask you this question. :)