One of my college professors put that suggestion like this: Write to an audience of intelligent 17 year olds. Ignorant of your topic and unwilling to put up with confusing writing, but curious and capable of understanding complex ideas.
When I followed that advice my writing was clearer and better balanced. I also found that the narrative in every piece (even technically orientated stuff) became stronger.
I don't write essay's any more, but it's still the standard by which I measure every email and comment I write.
I'm in the process of writing my thesis and one of my advisors asked me: "Who are you writing this for?". I had a few ideas, but I answered, "For him and our collaborators."
"Wrong! - You should be writing for the graduate student who will be picking up your work."
Any graduate student or even many professors will be on a similar level when exposed to something new. By explaining stuff at a relatively simple level, with enough intermediate steps to outline the method, most people can grasp how you did what you did.
Maybe not 17 year olds, but aimed at people well versed in mathematics, but not necessarily in that field.
When I followed that advice my writing was clearer and better balanced. I also found that the narrative in every piece (even technically orientated stuff) became stronger.
I don't write essay's any more, but it's still the standard by which I measure every email and comment I write.