Natural Frequency of an object and the phenomenon of resonance! I have read about the term natural frequency in quite a lot of places. But I haven't found an explanation as to what is vibrating. It was pretty awkward when I couldn't clearly answer my little sister when she asked me to explain natural frequency and resonance. While studying dynamic analysis, I have actually determined this natural frequency for a variety of systems. But when I really thought of it, I just haven't been to clearly define the term natural frequency. And this question further leads me on to the phenomenon of Resonance. I have heard that failure by resonance is the reason for soldiers not marching on bridges, and this phenomenon is the exact reason why beats occur. So the objective of this question is to explain fundamental frequency in terms of what vibrates and what causes the vibrations and to explain the phenomenon of resonance based on the above explanation.
EDIT: All the answers are helpful. But the objective, as I have clearly mentioned, is to make me understand. So I would appreciate it if you could give the complete picture, which I haven't got from any of the answers as of yet!
 A: The natural frequency (or frequencies) isn't about what started the vibration, it is a property of the object: it "prefers" to vibrates that way, and getting to vibrate another way is harder.
Take an object, say a bell. Hit with a hammer.
When you first hit it there are vibration of many different frequencies started in the material. Most of those are no where near the natural frequencies of the object and so will die away quickly. Those that are near the natural frequencies will last longer because vibration loses energy more slowing in those modes, so the natural frequency will persist longer than other modes. High quality bells and gong can ring at their natural tones for a very long time indeed.
Resonance concerns what happens when you don't just hit the object once, but continue to shake it steadily. Energy can build up in the vibration of the object and it will do so most effectively at driving frequencies near the natural (or resonant) frequency of the object.
Now, I've short changed you a little bit because I haven't talked about overtones, but that for another question.
A: Since you want to answer a small child, I'd just start with a weight on a spring, preferably with a physical demo at hand.  Show how it bounces at a specific rate regardless of how you initially stretch it out.  Then maybe show a different resonant rate when you change the weight, or length of spring.  That takes care of the "natural resonance frequency" part.
Then, maybe a bit more tricky: gently tap the weight (vertically) at the resonance rate and show the amplitude growing.  Then tap at some other rate and observe the amplitude collapsing or going pseudorandom. 
