[nobody9999]

>I kind of disagree. If I "parrot" (Accurately repeat) the original statement, it does not in any way demonstrate understanding, only memorization/note-taking.

>Restating, summarizing, or paraphrasing, shows that I understand sufficiently that I can describe it in my own words rather than memorization.

That's absolutely correct. Restating the concept(s) presented definitely provides confirmation that they have been heard and understood[0].

I'd only add that doing so may also alert the other party to a lack of understanding, requiring further discussion, which is arguably as or more useful than just assuming you are understood.

[0] See what I did there? :)