What exactly is captured in a Sample of the Nyquist-Theorem variety? I'm new to DSP and was thinking of sampling in the traditional music creation way, in that you capture a sound and play it back, warp it, etc., but when I thought about the Nyquist theorem, I realized that can't be what's happening when sound is being captured. 

If we treated a sound clip that is 1 second long as its own waveform, then it's 1Hz and according to Nyquist you'd have to capture it at least at 2Hz. That's only 2 snapshots for 1 second of sound.

What are those 2 snapshots capturing? Let's say it's 16 bits of depth. What can that combination of 1s and 0s capture exactly? I've caught that the bit depth determines how many dBs you have to work with (more range), but I'm a bit lost on the rest. Is it capturing a unique waveform tone? Is it specifically a Sine wave tone? Is it multiple tones? I'm having trouble picturing what's being sampled and how it's being accurately played back.
It might be better to think of Nyquist sampling as shooting fish in a bucket.

The bucket limits what is in the bucket by being only so large. This is like a band limit. We can only have so much variation.

Two samples is the very least number of samples we need to specify that 1 sec of 1 Hz sine wave, although intuition tells us we are on the edge.  Three samples for a second and half is a safer proposition.   How about 120 samples for 60 seconds of 1 Hz signal. If you look at the reconstruction formula for Nyquist sampling, it says you need a need an infinite number of samples to get that 1  Hz sine back.  The summation limits are plus and minus infinity.

In practice, we usually sample a bit faster than what Nyquist specifies. 

There are circumstances where one can sample less than what Nyquist tells us and there is a lot of activity in an area known as sparse sampling. 

To be honest, this was a terrible analogy. The mathematics is really more straightforward. Things like mathematical limits are hard to analogize.

It also turns out that a 1Hz sine wave is also a mathematical ideal.