To go as the crow flies is to take the most direct route somewhere. Going as the crow flies is the shortest path between two points.
This expression has to do with traveling—in a very specific way. If you travel as the crow flies, you've gone somewhere as quickly and directly as possible. A shortcut is a good way to go as the crow flies. A direct airplane flight with no transfers is another way to go as the crow flies. When you think of this term, imagine a bird flying in a straight line from point A to point B.