> Band limiting means that there's a maximum frequency. You can think of it as a limit on how fast the signal can change. There's only one possible way to draw a curve that goes through all the points without changing too quickly.

This was incredibly helpful for my understanding. This is the one corner of this story that was always fuzzy for me. In the video he seemed to be making this point when he drew silly stuff all over the screen but it didn't quite click. Thank you.