A picture is worth a thousand words, so here is a VERY rough animation of what is going on during an eclipse. You're stationed above the North Pole of the earth, watching the moon's shadow overtake the earth from right to left (West to East). Notice that an observer stationed on the spot to the far right only gets totality for a brief time, basically because the shadow is smaller at that point. For observers farther east along the path, the shadow's bigger cross-section produces more time in the shadow. This is maximized at a point called "greatest eclipse", which for the 2017 eclipse occurs near Hopkinsville KY.

This animation is very rough, with an extremely exaggerated scale, and does not show the effects of the rotation of the earth, which also serves to give noon-time observers a greater amount of time in the shadow.