I wonder if it is neutral (in a sense close to that no positive or negative things implied) when an American utters "that makes sense" after hearing an explanation. I would like to know if it is used as a neutral expression under normal circumstances. For example, is it understandable for a student to use "that makes sense" after the professor answered her or his question? Thanks.
I'm not sure I fully understand the question in terms of it being neutral, but yes, as an American, this is commonly used in lieu of "I understand"
I would say that yes, That makes sense is a 'neutral' response. It indicates that the student has understood the answer given, and doesn't have any followup questions on the same subject. It does not, by itself, indicate whether the student agrees with the answer - whether that's relevant or not depends on the question - and it would therefore be fair to call it 'neutral'.
A response of That makes perfect sense would be less neutral, and would probably indicate agreement with the answer.
A response of That doesn't make sense would be less neutral, and would indicate that the student either disagrees with or doesn't fully grasp the answer. They may have followup questions.
I wouldn't call it neutral. It is positive. It means "what you've said seems plausible" or "what you've said is cogent, or reasonable". It would be nice to live in a world where "that makes sense" was neutral :)