I believe that the ultimate proof that you understand something is when you can break it down to its essence and teach it to someone that's unfamiliar with the subject.
Sometimes we think we intuitively understand something, but only when we try to break it down, we end up realizing that we didn't really understand it in the first place, or that it was based on wrong assumptions.
And because we already think we understand something, we're very biased and breaking it down ourselves is always difficult.
So trying to explain a concept to someone unfamiliar with it that's genuinely interested is always a very good way to break something down to it's essence.
I find that writing your thoughts and ideas has a very similar effect, it's as if you're explaining something to an imaginary person.
It's also very hard to retain everything you learn, so writing it down for later reference is the best way to make sure knowledge doesn't get lost.
Writing also has a very iterative feel to it too, you can write incomprehensible ramblings about something when you have an idea, and rewrite it again and again during days until it's good enough, this fits very well with the way I think.
But most importantly, I enjoy writing.