As I understand it, Local Space is looking for the tracking target to change its position directly. When it is moved along with everything else, its position doesn’t change relative to the thing trying to track it. So as far as the Track To constraint knows, that Empty hasn’t really moved. With World Space, the constraint will look for any change of position relative to the whole scene.
Another way to think of it is this: Imagine you have a rock sitting on the surface of a planet. In Local Space (just looking at its position relative to the planet), it is sitting perfectly still. But the planet is orbiting the sun, so in World Space (relative to the whole solar system), it is moving in an elliptical path at 70,000 miles per hour.