Outer anchor point added using the Direct Select tool

Hello!

I had a new thing happen to me today, and I'd like to be able to explain it to my students. The problem is, I'm not exactly sure how to do that because I'm not sure of the purpose:

I wanted to demonstrate using the Direct Select tool to adjust only the bottom two corner widgets of a square. When I Shift + select the anchor points, everything acts as you'd expect. BUT, when I click+drag to select the bottom two anchor points and connecting line segments, a new anchor point appears outside of my square (you can see it as a tiny x on the bottom line or the bounding box in my first screenshot, then as a filled blue anchor point on the bounding box in the second screenshot).

When I hover over it, my Direct Selection cursor changes to a Select Anchor Point icon, and when I click on the new anchor point, it drags the selected objects around as if I was just clicking on the line segment to manipulate the shape.

I would like to be able to explain:

  A. Why the addition of the exterior anchor point?

  B. Does it have a special name?

  C. In what circumstances would I want/need to use it?

I greatly appreciate your help!