This is when I was eight or so, and it's the first aha! Moment that I remember. For the first time, I realized that = meant both sides were equal. Of course, I already knew that and paid lip service to it, but I had never really understood what it meant. In my mind, the LHS had had to be a computation of some sort, and the RHS had to be the result. I now knew that = meant that the two sides, whatever they may be, were the same thing.
It's very difficult to transmit this insight and have the receiver realize that this is a nontrivial insight. In my experience, only those who have had analogous experiences and those who teach math really get what I'm talking about.
I had an analogous experience when learning programming for the first time related to the return type of a function - that if you have a function like "int myFunction()" it in some sense "is" an integer, and so the function call can be substituted anywhere that you could use a literal integer (like 3).
Of course it's not quite that simple in most programming languages since impure functions can have side effects that have nothing to do with the return value, but it was still a helpful realization.
Sometimes our minds suddenly "click" and we see a topic in a new light. Or sometimes we think we understand an idea, think it's stupid and ignore attempts to explain it ("yeah, I already know that"), until we suddenly realize that our understanding was wrong.
This kind of insight is supposedly hard to transmit, but it might be worth a try!
So, what kind of important and valuable insights do you wish you had earlier? Could you try to explain briefly what led to the insight, in a way that might help others get it?