For me, I think the best way to put it is that I expect to learn something useful from each essay. I mean, why else would I spend hours reading through them? In some ways, that’s really the only expectation I have. Of course, nobody can learn much from an essay that is more or less incomprehensible, whether it is due to bad English writing, poor mathematical notation, or weak logical argument.
There are some usual constraints, of course. For example, your essay obviously should be related to the course, and you should not plagiarize others’ work. Keep in mind that, generally, “double dipping” is not allowed, i.e., you cannot submit the same work to receive multiple academic credits.