First published April 29, 2020.These are my thoughts on what makes writing good. Much of it was inspired by Evan Chen and Paul Graham.
Whenever you've written something general, the first thing you should try is seeing whether it applies to specific cases. These "test cases" will usually be what you deem important to you. If you're a programmer you'll think "does this apply to programming?" If you're a mathematician you'll think "does this apply to learning/teaching/doing math?"
The things you decide to use as your test cases often speak to your values and experiences.  Work is what smart people see as the good of the world, and school is a prime example of what's wrong with the world. 
And what if what you wrote doesn't agree with your test cases? The best thing to do would be to fix what you wrote so it does fit. If what you wrote is mostly true, then making the write distinction is probably enough. And if you can't salvage what you wrote, you should probably delete it. 
Writing is keeping good thinking in posterity. While it's often hard to differentiate a good idea from a bad idea until you're well into it, it is not hard to differentiate an idea from the lack of an idea.
So don't force yourself to write. Instead you should be compelled to write by some realization. These realizations are usually not sudden but have been gradually and not entirely consciously happening. The breaking point is when you decide "I have to put this down somewhere, or else I'm going to forget." Usually it's when you reach this breaking point that you feel compelled to write.
Ideally you should be able to drop unimportant stuff like schoolwork when this breaking point is reached.  But if you can't immediately stop what you're doing, at least put your focus onto your realization. As an analogy: If you've got water in your hands and can't find a bucket to put it into, at least try to keep the water in your hands.
This may not apply when you're doing something important, but when you're doing something important that can't be stopped, your mind doesn't often wander enough to the point where you realize you have something you need to put on paper.
You can't write well about something without caring.
What I originally thought I would write was "You can't write well without writing about something important." But I think there's an important distinction to be made: important things have big effects, and things that matter affect you in a way that you care about. For instance, both heuristics would succeed in determining that your English essay is not good writing. But only the first would succeed in determining that your character analysis on your favorite film can be good writing, and the second would mistakenly determine that the essay you have to write about the NCAA's decision not to pay student athletes is good writing. This distinction is important in that it hammers home the idea that good writing satisfies yourself, not your responsibilities.
What you write will reflect the framework that you view your life in. This isn't something you can avoid, and nor is it something bad.  In fact the synthesis of (useful) perspectives has another name: learning. And perspectives can't be synthesized unless shared, and perspectives can't be shared unless written or said.
You're not writing to please the world. You're writing to please yourself. And incidentally other smart people in your field will also be pleased.  This means that if your writing is meaningful, it will really only specifically apply to a certain group of people. This is both horrifying and exciting: What you write may not even apply to a large portion of smart people, but that also means there's so much fertile land waiting to be tilled.
It's actually okay not to have an audience when you're writing. The most important benefit of writing by far is that it actually forces your thoughts to take form. It provides clarity. This is why keeping a diary isn't useless. This is why clarifying something in your head is meaningful, even if it doesn't end up making it out of your head.
That being said, there are some benefits to making your writing public. The first is that it puts another perspective out there. The second is that it can create a dialogue - perhaps not one that you can see, but instead one with your writing and someone else's thoughts. It also forces you to make your writing say-able and provides some level of quality control - if you're going to put it out on the web, you might as well make it something worth reading while you're at it.
I think that a lot of people have the wrong model of what revising really means. Revising isn't making something have bigger words or artificially inflating the length of your essay because you don't think your English teacher will give you an A unless you have 5 pages. Revising has two goals: To come closer to the truth and to make what you write sound like what you would say.
You won't write something completely true. But you can do your best to get as close as you can. One of the most common things that happens during revision is noticing something you said isn't true or isn't substantial. People will try to cover it up or make it sound more convincing to no avail - false writing is bad writing.  The primary objective should be to make something false into something true, and something insubstantial into something substantial. For the former a clever distinction is usually what's missing, and for the latter deleting what lacks substance is the first order approximation of the correct thing to do.
The only convention you should follow is making your writing say-able.  There are plenty of grammar rules English teachers teach you, but the only ones you need are the ones that make your writing seem natural. This means you split the infinitive if it would flow better. And so on.
One of the worst habits English class teaches is to not use contractions. In fact you shouldn't write a contraction out unless you would say it like that. 
So do not let yourself be held accountable by a set of standards that don't even determine good writing in the first.
If I have to boil it down to one sentence it's this: You should feel that there's a purpose to what you're writing. It doesn't have to be clearly defined. You don't even have to know what it is. But there has to be something there that makes you want to write whatever you're writing. Everything else will come after.
In fact everything else is just a coy way to say this. You have to actually apply what you wrote to reality for it to be meaningful. There's no purpose to writing an essay for English class or writing about something that doesn't matter to you. A unique framework actually makes it worth sharing your ideas. And when you revise you do it for a reason: to come closer to the truth, and to write something you could say.
 This is probably why people who write well also know where their priorities lay. It's inevitable that they figure their priorities out when their writing reveals them.
 The best place to go hunting for problems in the world is school. Especially if you're looking for reasons artificial stuff is bad.
 This applies to entire essays too - if you find that you wrote something that isn't true or substantial, toss the entire thing out.
 This is one of the reasons that the people who don't pay too much attention in school end up being the most thoughtful.
 Unless if your framework of the world actively goes against reality. Then that's definitely bad.
 I find that the intelligence of someone's audience says a lot about their intelligence too.
 This is probably something that's been hammered in by English class - not once has your teacher just told you "there's no substance to your writing." They instead focus on the symptoms of soulless writing, such as overly verbose sentences or just being a slog to read.)
 "Say-able" literally means something you could say. As a rule of thumb, writing is good if you find yourself saying parts of it out loud. This is also the reason people write stuff like "stuff" - it's because that's how they would say it.
 The most common reason to write out a contraction is probably for emphasis.