More distant galaxies have larger shifts, which means they are moving away even faster.
This tells us that the Universe is expanding . All we need to know is how fast a distant galaxy is moving away from us, and how far it has gotten. But it is a little trickier to get the distance. We could measure the distance to a nearby source using some other method, then we could figure out how far away a more distant source is just from its brightness. For example, if the nearby source looks 100 times brighter, it must be 10 times closer since 10 squared equals 100.