The first caption shows the focus and directrix that will be used to construct the parabola. As you know a parabola is a set of points equidistant from a line called a directrix and a fixed point called a focus. You construct a perpendicular to a point on the directrix. Find the midpoint between that point and the focus a construct a perpendicular. Where these two lines intersect will be the traces of the parabola.

Now the trace is complete and you can see the parabola in red. This is constructed by animating the abitrary point highlighted on the directrix.

Now you can see what happens when the tangent line of the parabola is traced. It is easy to understand the definition of a tangent line by looking at this construction.