There’s definitely something about the process of writing things down physically that seems to hardwire information to a degree. As a brain guy, I guess I’m supposed to have all the answers on why that works, but I don’t 
I think the short answer is probably that many senses are being included at once: visual and tactile. There’s probably a bit of inner auditory stuff going on as well as we talk to our inner selves through the process of writing.
When I was re-writing my notes from class, I wasn’t rewriting them word for word, I was compressing them, making them more pinpoint accurate, comparing them with things previously learned and how they fit in together. I still do that process now with learning new things in my new work, constantly testing how things fit together.