A great question! The Moon does indeed "carry" its shadow along with it, as it moves in its orbit around the Earth. And whenever that shadow happens to scrape across the Earth, we have a total eclipse! (Of course, you have to be in the Path of Totality to see the total eclipse, and you have to use eye protection whenever the eclipse is not total - regardless of whether...
The Sun and Moon both appear to "rise" in the east, and "set" in the west. But as you can see in our video of the Moon's shadow sweeping across the USA for the 2017 eclipse, you see that the shadow plainly traveled from west to east across the country! This is a very good question, because it shows how solar eclipses take us out of our normal experience....
Whenever eclipse geeks are talking about their calculations, they always need to make sure they are careful to distinguish as to whether they're talking about "magnitude" or "obscuration". In case you'd like to understand this, too, here is a quick explanation. I'm going to use the word "percentage" below, but if you want to substitute "fraction" or even "amount" (so long as you understand what you mean by that word),...