One concept that is fairly easy to explain is smoothing filters. After a signal has been converted from digital to analog, it's a series of stairsteps. The smoothing filter smooths out the stairsteps to create a continuous waveform, but more importantly, re-create the original waveform.
Here's an analogy. A baseball player hits a fly ball to center field and you're in right field. Plot the height of the ball every 10 ms. This produces a series of points that correspond to the height. If you connect these points with a line, you will describe the ball's trajectory. Now, you might think "so if the points are closer together, the arc will be described more accurately." And that's true, BUT like a baseball audio doesn't move in a series of straight lines from point to point, and a smoothing filter recreates a smoothed curve based on the points. If you compare that smoothed curve to the ball's actual trajectory, you'll find the correlation is for all practical purposes identical.
The smoothing fllter is an important part of the "sound" of digital audio. Many people think the reason why DSD sounds more "analog" (whatever that means, LOL) is because the sampling rate is so high - a minimum of 2.8 MHz, with 5.6 MHz also being common - you can basically filter out the clock by twisting a couple wires together and hanging them across the output. Well maybe not quite, but you get the idea.
Those who think sample rates need to be much higher would make the argument in the baseball analogy of "Well, what happens if the ball hits a fly in between the two points where it's measured? Wouldn't that knock it off course somewhat?" The counter-argument would be that even at 44.1 kHz, the distance between the two points would be sufficiently close to take that into account.