Am not sure if this is indeed what you are talking about but if it's the realisation that any song can be played in any key, and that you can mechanically 'transpose' (I think of it as shifting) any song in whichever key you want and more fundamentally, a tune is made of intervals, that was a big aha moment for me too.

The next was discovering the tonal center or 'root' of a song. A lot of gears clicked into place at that point.