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Okay, thanks for the explanation. I have another question. Why is it that the shadow cast by the moon on the land is only between 50 and 100 miles wide?
Since the moon is supposedly 2,159 miles wide, it should cast a much wider shadow.

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The size of the umbra varies from one eclipse to another mostly due to how close the moon is to the earth each time. The distance from the earth to the moon is constantly changing since the moon's orbit is not circular but rather it's elliptical or parabolic, really. Kind of like a hula hoop being twirled around your waist.
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That's the umbra, or the totally dark area of the moon's shadow. If the moon were further away from the earth this time, the umbra would be smaller. And if it were far enough away, there would be no umbra at all because its total shadow would reduce to a point before it reaches the earth's surface. That's what happens when we have an "annular" eclipse, when the sun is seen as a ring all around the moon.
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This time, I expect many thousands of people viewing this "Great American Eclipse" to see the "Diamond Ring" effect, when just before totality, one speck of the sun's perimeter keeps shining through some crevice or valley of the moon's surface and everyone sees the circular center which is the shape of the moon, looking like the open space in a ring where you put your finger, but the sun's shine splays out in one place on the "ring" as if it were a huge diamond mounted there.
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The width or diameter of the moon casts a shadow toward earth that has a two-aspect conical shape. One cone is the total darkness where the sun is totally covered by the moon, and this shadow gets smaller the further away from the moon you go. The open end of the cone is the perimeter of the moon where the light side of the moon (lit by the sun) transitions to the dark side of the moon (in the shadow side). The point of this cone is the very end of the moon's shadow where a viewer would see the sun emerging all around the moon.
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The other cone is one where the moon itself is the point end as it were, and the cone gets wider moving away from the moon and away from the sun. This is what people on earth will see when they are far from the total eclipse path, as far away as in South America where the moon will only obstruct some small portion of the sun, like 1% for example. Beyond that point, where the moon obscures nothing of the sun, is outside this second conical shadow.
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I don't really like this picture because it does not show the shadows accurately considering the displayed size of the sun. It's not to scale so you have to imagine the sun much further away for this to make sense. Think of the sun about 10 feet to the left and it's a little closer to reality, however that's just an approximation because the sun is much larger than that and much further away, but perspective wise, this size and 10 feet isn't too bad. The point is, the top line of the umbra should be pointing at the top edge of the sun. Likewise, the top edge of the earth's shadow should be pointing at the top edge of the sun, too. But this is just for the sake of names, where it shows the umbra (full shadow) and the penumbra (partial shadow). 
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Here is another picture, with a little different style:
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They admit the diagram is not to scale! That's correct!! 
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The sunlight appears to be coming in parallel lines (they're not actually parallel but they APPEAR to be). That's why the moon's penumbra appears to be a cylindrical shape, when in fact it is a conical shape with the moon at the small end of the cone. Likewise, the earth's shadow (not shown here) is conical too, with the earth being at the small end of the cone and the cone getting larger as one moves away from the earth on the shadow side away from the sun.
.

.
The size of the umbra varies from one eclipse to another mostly due to how close the moon is to the earth each time. The distance from the earth to the moon is constantly changing since the moon's orbit is not circular but rather it's elliptical or parabolic, really. Kind of like a hula hoop being twirled around your waist.
.
That's the umbra, or the totally dark area of the moon's shadow. If the moon were further away from the earth this time, the umbra would be smaller. And if it were far enough away, there would be no umbra at all because its total shadow would reduce to a point before it reaches the earth's surface. That's what happens when we have an "annular" eclipse, when the sun is seen as a ring all around the moon.
.

.
This time, I expect many thousands of people viewing this "Great American Eclipse" to see the "Diamond Ring" effect, when just before totality, one speck of the sun's perimeter keeps shining through some crevice or valley of the moon's surface and everyone sees the circular center which is the shape of the moon, looking like the open space in a ring where you put your finger, but the sun's shine splays out in one place on the "ring" as if it were a huge diamond mounted there.
.

.
The width or diameter of the moon casts a shadow toward earth that has a two-aspect conical shape. One cone is the total darkness where the sun is totally covered by the moon, and this shadow gets smaller the further away from the moon you go. The open end of the cone is the perimeter of the moon where the light side of the moon (lit by the sun) transitions to the dark side of the moon (in the shadow side). The point of this cone is the very end of the moon's shadow where a viewer would see the sun emerging all around the moon.
.
The other cone is one where the moon itself is the point end as it were, and the cone gets wider moving away from the moon and away from the sun. This is what people on earth will see when they are far from the total eclipse path, as far away as in South America where the moon will only obstruct some small portion of the sun, like 1% for example. Beyond that point, where the moon obscures nothing of the sun, is outside this second conical shadow.
.

.
I don't really like this picture because it does not show the shadows accurately considering the displayed size of the sun. It's not to scale so you have to imagine the sun much further away for this to make sense. Think of the sun about 10 feet to the left and it's a little closer to reality, however that's just an approximation because the sun is much larger than that and much further away, but perspective wise, this size and 10 feet isn't too bad. The point is, the top line of the umbra should be pointing at the top edge of the sun. Likewise, the top edge of the earth's shadow should be pointing at the top edge of the sun, too. But this is just for the sake of names, where it shows the umbra (full shadow) and the penumbra (partial shadow).
.
Here is another picture, with a little different style:
.

.
They admit the diagram is not to scale! That's correct!!
.
The sunlight appears to be coming in parallel lines (they're not actually parallel but they APPEAR to be). That's why the moon's penumbra appears to be a cylindrical shape, when in fact it is a conical shape with the moon at the small end of the cone. Likewise, the earth's shadow (not shown here) is conical too, with the earth being at the small end of the cone and the cone getting larger as one moves away from the earth on the shadow side away from the sun.
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No, that doesn't work at all. There is no "cone." That's not how light works. I did a little experiment this afternoon, and the shadow was the same size as the object that I put between the flashlight and the surface on the other side of the object. Light does not travel the way you have described it.