This is a very specialized tool that allows you to add a point at the intersection of an imaginary line through an existing point and another line or curve. The imaginary line will be perfectly vertical or horizontal.
Let's step through the process, so it makes more sense. This is a bit confusing.
Select point for alignment means to select the point that will have a line drawn through it.
Next select whether that line will be Horizontal or Vertical.
You will see a dashed line drawn through the point you selected.
Next you will select a line or curve that intersects that dashed line. The intersecting shape can be a line, curve, polyline or reference shape.
In the image below, a circle was chosen.
When you select Continue, the point(s) will be added.