How I think it works is like this:
Whenever you add an object, that object's origin will be placed where the 3D Cursor is. When you open Blender, the 3D Cursor is at x:0 y:0 z:0, so the origin of whatever object you add will be at 0,0,0 the perfect center of the scene.
The origin is at the center of the object, 2D, or 3D objects have different geometric origins. A cube for example, has its origin at the center of the object, that is why it is half in the z+ and half in the z- sides of the grid
...and when you use the Active Tool from the Toolbar, it starts to make the surface of the Cube and snaps it by default to the Surface of any Object, or if there is nothing to snap to, it falls back to snapping to the Grid. You can change the settings to start at the Origin (center) of the Cube (or other Primitive):
This way of Adding Primitives is being shown later in this lesson.
What almost everyone does is move the cube in edit mode in grid unit in Z to leave the origin at the bottom and the cube flat with the grid. All of it is just personal preferences, don't think about it as wrong or right. I myself have the tendency to work above the grid because I feel like it's the floor, I don't like things going under it. But some people work as if the gird isn't even there and things go under and that drives me crazy. I like using the grid as a floor baseline reference point, some insane people don't.
