Explaining UV radiation to a 6 year old My (just completed) PhD involved a considerable amount of research involved with the detection of solar UV radiation.  This generated quite a bit of interest, especially when I was conducting my experiments outside.
A friend's 6 year old was most fascinated, but could not grasp the concept of UV radiation, primarily as she could not 'see' it. She understood the importance of protecting oneself from too much UV (this is a big thing in Australian schools).
On reflection, it occurred to me that a lot of people don't truly grasp what UV radiation actually is, despite knowing of the risks involved with overexposure.  Conversely, I know and understand the technical side of it, but struggle to put it in simpler terms.
What is a simple and meaningful way of explaining UV radiation?
 A: First, try and see if you can get the 6 year old to think about "what if there are colors we can't see"? Explain to her that the color we see is the color of "light".
Now, show her a remote control, and press some button. There's an IR bulb up front, ask her if it flashes when you press the button (it shouldn't). Now, use a phone camera to look at the IR bulb, most phone cameras will show white light when the button is pressed. Explain to her that the light coming from the remote is "invisible", in the sense that it's of a color we can't see. However, the camera can see it because the camera sees slightly more "colors" than we can, and when it tries to display it it shows it as white.
Explain to her that this is "infrared" light, a light that is "more red than red itself". Whenever someone turns on the TV, a light signal is sent to the TV. (You may want to explain that this light has some "bending" capabilities, but that's not entirely necessary).
This ought to get her past the mental block when it comes to "light that isn't light". Mentioning that some animals see more/less colors than we do helps.
Now, talk about the spectrum:

Explain that the light that we can see is a very small portion of the kinds of light that actually exist. The spectrum is what she sees when she looks at a rainbow, but it really doesn't "stop" at red or purple; she just can't see it.
If you wish, you can then talk about radio waves, and how they are light that can easily "bend" (i.e. diffract). Talk about X-rays, which is light that can pass through skin but not bones. This can actually lead to an interesting side track where you explain how an X-ray is nothing but a photograph with a different kind of light.
Once you reach here, it's easy to explain UV. Mention that while the sun emits a lot of visible light, it's not limited to the visible spectrum and emits a significant amount (much less, but not negligible) of UV and IR as well. 

You can actually extend this to sound as well, talk about how there are sounds we can't hear. For that matter, sounds just outside your hearing range will be clearly audible to most six year olds. If you can generate increasing frequencies from your computer (It's actually possible for our vocal cords to work in the inaudible ranges, but it takes some practice to get that to work so it's just easier to use a computer), you can both show here that different people/ages have different frequency ranges1, and that there are sounds that even she can't hear. (to do the latter you may want to set up a microphone and have it show the amplitude on the screen or something). Similarly, you can go to lower frequencies (and show the transition from invisibly fast vibrations but audible sounds to visible vibrations and inaudible sounds in a string instrument or possibly a rubber band). It's a good opportunity to explain how a dog whistle works, too.
The concept of there being light that we can't see and sound that we can't hear is a really amazing one when one hears of it first. I certainly was intrigued by it when I learned about this as a child.
1. This may not be so easy and may not be desirable, see Cleonis' comment below
A: First of all explain what radiation means.
One could use a flashlight and demonstrate that the light comes through the air without anything bringing it, it is not like a rolling ball, it is not like the waves in the sea, light from the flashlight is radiation: it comes out all in a circle from the center of light. That center in the flashlight is a lamp, heated by batteries so that it give off radiation in the form of light. 
Then one needs an infrared heater: a wood stove would do, or an electric  kitchen stove. Light up one of the plates/spirals and bring her hand close to feel the heat coming out. This is also a form of radiation coming out all around but our eyes cannot see it because they are not meant to see radiation at that range. It is our skin that can "see" it, feel it.
Then explain that the sun is a great source of radiation like a huge furnace thousands and thousands of times stronger than any stove on earth or any batteries. It radiates away into heat radiation, into light radiation and into ultra violet radiation which like the heat radiation our eyes are not made to see. When it hits our skin it turns into heat radiation plus extra destruction of our skin's cells because it is very strong radiation that not only burns, as heat/infrared  radiation does, but also destroys cell structures .
One could then introduce a graph that shows the radiation coming from the sun, and explain how the strength in terms of damaging the skin is related to the x axis and the y axis tells us how much of each type of radiation hits us when we sit in the sun.

A: Kids are familiar with balls, colors, and temperature, so we might approach this using a particle model through the use of an analogy. 
Light is kind of like a stream of balls. Red-light balls are cool, Blue-light balls are warm, and UV-light balls are really hot.  We can see light in the rainbow (Visible Spectrum) because our eyes like the temperature of those balls. Some balls are too cold (IR, etc.) and some balls are too hot (UV, etc.),. Getting hit by too many balls (looking at bright light) is bad, even if the balls are not super hot. Catching a very hot ball will burns our hands.
The take-away is that there are colors outside of the rainbow we cannot see. Each color has a certain photon-energy. And UV light has high-energy photons which can hurt us.
Note, I have just presented an analogy I believe a six year old could understand. PER recommends using demonstrations, experiments, and question techniques to help the child build the model for himself rather than just telling him. 
A: Your best bet is to show her a video of thermal imaging.  The idea that there are heat waves and other things we can't see is very clear when you show a kid how a thermal imagining camera can see in the dark.  There are a lot of youtube videos that might be good for demonstrating the concept.  Once you try to explain EM spectrums or the concept of radiation you've already lost the battle.  Go simple and use a visual.
If you have a spare digital camera around you could remove the IR filter and give a live demo.
While I like the idea of using a rainbow as a visual or "other colors you can't see" most kids will think you're just playing a game with them like an imaginary friend who is colored UV.  It won't really sink in that these things exist unless you show them there is a world beyond what we can see with our eyes.
A: Do you have any sort of blue light that's at the edge of visibility, like a black light or some LEDs? You should show her that, and tell her the reason it looks like it's hard to see is because it's actually too blue for our eyes. Tell her if it were more blue, we couldn't see it, but there would still be light. You can also point out that orange-red light seems to be hotter (heat lamps), and that this is because the light that is "too red" for us to see is also being shined along with the visible part of the orange/red light, and that light is very easily absorbed as heat.
(Take it further, but this is a start. She will probably enjoy relating the concepts to things she can observe.)
A: Light, the sun and colors combine in one thing which 6 year olds know: rainbows. And that makes it easy to explain what UV is. Why are there two edges, inside and outside, on a rainbow? Why is there no color outside red or inside violet? Well, there are, but you can't see them. They're all colors in the sunlight, but not all colors that your eye can see.
You can even ask her to draw a rainbow, and then - with an invisible crayon of course - draw an invisible extra UV band on her rainbow :)
A: Don't explain the diagrams to her, she might find it confusing. Try to make the UV like a dangerous alien or something that harms humans. Children can relate better to fictional characters and stories, and this makes it easier for them to understand.
