Every depiction I have seen shows the Eclipse path of totality travel Eastward from Oregon. Why Doesn't the path travel Westward from South Carolina as the Earth rotates Eastward? Shouldn't the Totality follow the Path of the Sun?
The answer posted by Sammy Gerbil is quite wrong. The passage of the eclipse from west to east has nothing to do with the sun overtaking the moon in the sky.
Sammy does correctly point out that, as viewed from above, the moon is circling the earth in a counterclockwise direction. And that means it is travelling from west to east. It is in fact travelling quite fast: about 2200 mph in fact (relative to a fixed earth), as you can verify by some simple computations. And that is also how fast its shadow is traveling.
The rotation of the earth however, being in the same direction, tends to counteract the motion of the shadow, by around 800 mph at the latitude of the eclipse. So the effective speed of the shadow across North America was close to 1400 mph, from west to east.
There is a very good animation of this on the Wikipedia website from which you can see at once that I have calculated this correctly: https://en.wikipedia.org/wiki/Solar_eclipse_of_August_21,_2017
EDIT: interesting that if you could rev the earth up to reduce the day to 11 hours, then the totality of an eclipse could last almost all day.
As Earth orbits the Sun, the Sun appears to move to the east against the background stars by about 1°/day --- completing its apparent route around the ecliptic in about 365 days.
As the Moon orbits the Earth, the Moon appears to move to the east against the background stars by about 12°/day --- completing its apparent route around the sky in about 30 days.
During a solar eclipse, the Moon "overtakes" the Sun against the background stars, traveling from the Sun's west side to its east side over the course of roughly 1/12 day = 2 hours.
When you are observing totality, people to your west have seen totality already, but people to your east have not seen totality yet.
Earth's rotation, which causes the Sun, the Moon, and all the stars to move from east to west at a rate of approximately 360°/day, is a distraction. Think instead about the apparent motion of the Sun and Moon compared to the distant background stars.
Like the Sun, the Moon travels from east to west across the sky. However, the Moon travels slightly slower than the Sun, because of its rotation around the Earth.
Looking down from above the north pole, the Moon orbits anticlockwise, the same direction as the Earth rotates. But because its rotation period is much longer - about 27 days compared with 1 day for the Earth's rotation - this makes only a small difference to its speed across the sky.
As the Sun overtakes the Moon in the sky, the shadow of the Moon travels from west to east.