I'm not wondering what the formula is—I already know that. For a parabola in standard form of $(x-h)^2=4p(y-k)$ I know that the focal width is $|4p|$.
But what does that mean, conceptually?
What does that distance, $|4p|$, represent? If I were to graph the parabola, would that distance be some measurable value between the focus and something else? Or between the vertex and something else? It's easy enough to solve what the focal width is; I just want to know what the point of it is. Can someone please explain focal width, as a concept, in plain English?
This is the length of the focal chord (the "width" of a parabola at focal level).
Let $x^2=4py$ be a parabola. Then $F(0,p)$ is the focus. Consider the line that passes through the focus and parallel to the directrix. Let $A$ and $A'$ be the intersections of the line and the parabola. Then $A(-2p,p)$, $A'(2p,p)$, and $AA'=4p$.