A galaxy is a system of millions or billions of stars. There are an infinite number of galaxies in our universe.
Look at the night sky. You can see other galaxies with your naked eye. From planet earth in the Milky Way Galaxy, you can see the Andromeda, 2.4million light years away.
The distance between any two galaxies grows with time, creating an illusion of mechanical movement.
But the galaxies themselves never move. Motion is an illusion. To try to catch something would be like catching infinity. All that is, is here and now.
Below: working on explaining this concept:
catchinginfinity.com 