One thing I've discovered (after over 30 years of teaching) is that the process of understanding is extremely mysterious. You can explain something in a perfectly grammatical and unambiguous way to someone and they'll look at you with glazed eyes understanding nothing; on the other hand you may tell them some kind of heuristic which isn't really the whole truth at all, and suddenly they'll "get it" more or less completely.
The moment of understanding seems to be some sort of chaotic event - like a phase transition, maybe. But it's certain that different people understand best by precise explanation or maybe pictures or perhaps examples, etc. I think that a major communication skill involves understand that and taking advantage of it. (Of course, if you are lecturing to a group, you have to compromise this somewhat, but it still applies.)