Any telescope, even the one Galileo used 400 years ago, efficiently collects the light from the universe, allowing us to see more clearly very distant and otherwise faint things. That light travels to our telescopes at the speed of light, and while very fast (300,000 km per second or 700 million miles per hour), it does take time to reach us from deep space. Sunlight takes a little over 8 minutes to reach Earth, the nearest star's light takes over 4 years to reach us, and from a distant galaxy it could take many millions of years to reach us. So we do see those distant galaxies as they appeared in the past, millions of years ago.

This is a great question of any scientific investigation: are we finding lots and lots of phenomena that were unexpected or mostly just getting a much better look at what was anticipated? The Hubble has certainly allowed many discoveries, for example, it’s helped us detect many supernova explosions, which are unpredictable. However, supernovae are not new phenomena. But by studying them with Hubble and other telescopes, astronomers arrived at the very unexpected conclusion that the Universe is accelerating in its expansion, rather than slowing down from the mutual gravitational attraction of galaxies. In my opinion, that’s a real biggie, and a good general response to the question: what we discover in our work is often not wholly unexpected or a new phenomenon, but often in the grander scheme, we frequently reach conclusions that alter the next generation of expectations.