It does mean "understand or extract", but (importantly) it also means that the student will remember these particular points in the future.
He made a lot of valid points about development. That's what I take away!
(One student said this after hearing a speech. From the context, I can say he wanted to praise him(The Speaker))
What does "take away" mean here? I think he meant "understand or extract " in the place of "take away" but mistakenly used that phrase(However, I also saw a professor using it that way).
It does mean "understand or extract", but (importantly) it also means that the student will remember these particular points in the future.
I'm not a teacher of English, but I have spoken it for (almost) all of my life....