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!