"Explanation" in Eliezer's post 'Fake Explanation' has the first meaning, about reason and cause.

Fake explanation is also an incorrect description, so both senses you listed qualify. Explanation of a reason for something is also a description of that reason.

"Explanation" in my post 'Great Explanations' has the second meaning, about illustration, exposition, or demonstration.

It still seems mostly impossible to give adequate explanations in this sense. For highly technical topics, a fair share of difficulty is in understanding what the concepts are, so you won't be able to see what the relevant facts mean without already going a long way towards knowing why they hold.