In the case of Moiré patterns in pictures, we have lines in the real world that need to fit into pixels that fit a larger area than the Nyquist rate of those lines. The Moiré effect in pictures is just the interference pattern caused by this aliasing.
If you look at just a column of the image, and imagine the signal as being the brightness varying over the Y coordinates, you can imagine the mortar being an occasional regular pulse, and when your sampling rate (the pixel density) isn't enough, you get aliasing: you skip over, or overrepresent, the mortar to brick ratio, variably along the signal.
Now if you look at the graph in that picture, doesn't that look awfully similar to what happens if you try to sample an audio file at an inferior rate for display purposes?
In fact, try it right now, download Audacity, go to Generate>Tone, click OK with whatever settings it's fine, press Shift+Z to go down to sample level zoom, then start zooming out. Eventually, you'll see some interesting patterns, which are exactly the sort of aliasing caused by resampling I'm talking about: