Here I want to explain musical understanding as an ability to hear and recognize musical syntax. It serves as a useful starting point for thinking about music education, especially for children.
Music is like a language in some ways, and unlike it in some other ways. One of the similarities is that music has a kind of syntax. The meaning of things like a C major chord will depend on what comes before and after that chord. A progression such as C major, G major and C major creates a musical syntax of tonic, dominant and tonic. If we hear Gm C F, that same C major chord is now a dominant instead. The meaning of the chord depends on the context, thereby creating this syntactic effect.
If you can hear progressions like that and label them correctly, you are well on your way to understanding how music works. You can know on a purely theoretical level that in the key of C major, G is the dominant chord, and in F major C is the dominant chord. But knowing that without the ability to hear it and recognize it is far less useful than being able to hear it without being able to explain what a dominant is on a theoretical level. One could object: why call it "syntax" instead of chord functions? Chord functions are one type of syntax; scale degrees are another; pulse and meter are yet another. Syntax specifies what they all have in common: their meaning depends on the context. The note C is the resting tone of C major but the third scale degree of A minor.
The primary reason for talking about music like this is because of the implications for music education for children. An example is that learning to hear and recognize various musical syntaxes, such as a resting tone, needs very little general language ability. We don't need a grand explanation of what a resting tone is in terms of music theory; instead it's just the label of this sound that feels like we come home, or at rest, when we hear it.
Here is an example from a teaching experience of mine.
I had a student around 8 years old, and we were working on hearing tonic and dominant. To cut a long story short, I teach that by singing short melodic patterns that outline those chords together with the student in a call and response fashion. After a while, I introduce the terms tonic and dominant as names for the notes that sound like this and notes that sound like that. Finally, I make a sort of quiz where the student tries to guess which pattern I sang, the tonic or the dominant.
The mother took part in all the lessons, and by the time of the quiz she got confused. She could not understand what her son was hearing. How did he know when it was a tonic or dominant? So she asked me: What are we listening to? Is it like major or minor? What is this tonic and dominant thing?
Well, how do you explain that with words to someone who is not educated in music? It is surprisingly difficult!
"OK, well, there are things called keys, like C major."
"Wait, what is that?"
"Well, a key is a collection of notes that make up a kind of musical space... eehh, I don't know, man!"
But for her son, tonic and dominant were clear enough. He didn't know about keys, harmony or different scale degrees. In fact, we had just been singing and playing around. But his ear was capable of picking up the meaning of the sounds, and I just gave him appropriate labels for that meaning. With that basis, I can introduce sheet music by just transfering what he can sing and hear, into how it looks on a page. Similarly, when learning chords in all keys, you just start on a note and sing the tonic chord and then find the keys that sound right. No explanations of different accidentals, different key centers are neede to begin.