When you look at a galaxy or a star, what you are seeing is how it looked when the light left it. The farther away the object is, the farther back in its history you are seeing. You could be looking up at a star that no longer exists.
Suppose a very massive star, with a lifetime of only 50 million years, is 100 million light years away. Now, suppose that the star we see looks like it is 10 million years old. When did the star go supernova? When will we see the supernova event?
Think of the light signal we see as a movie being projected toward us from a screen. The signal travels at the speed of light. The image from the screen gets to us just a bit earlier than it gets to the person sitting behind us. In everyday life, his difference in time is so small that we are not aware of it. When dealing with the vast distances in the universe, the time difference matters. This diagram illustrates what we would see if we could see the entire beam of light coming from the star, from the side. If the star looks to us like it is 10 million years old, that means that the light that left the star when it was born passed us 10 million years ago (except, of course, for the photons that entered our eyes, reflected off the Earth, etc.).
If the lifetime of the star is only 50 million years, it has already blown up in a supernova event. The train of light that is the signal from the star while it was alive is 50 million light years long. We will see the supernova event 40 million years from now. The light signal that comes from the remnant of the star after it blew up stretches over 60 million light years. The star blew up 60 million years ago.
Now, consider a second scenario. Suppose you are looking at two stars, and they appear to you to be the same age. Which of the following statements could be true?
This could clearly be true. Consider two stars that are 50 million years old and 50 million light years away. The light emitted from both stars when they were newborn would be reaching us now, and they would look the same age.
This statement could not be true. If star A and star B were both 50 million years old, and star B was closer than star A the light from star B would have already passed us. They could not look the same age to us.
This statement could not be true. If star C was older than star A, but they were the same distance away, the light that star C emitted when it was born would have already passed us, and it would look older than star A.
This statement could not be true. If the closer star was older, it would appear older, since more of its light would have passed us.
This statement could be true. For example, if star A was 50 million years old and 50 million light years away, it would look newborn to us. If star A was 60 million years old and 60 million light years away, it would also look newborn.
Please watch this tutorial on Lookback Time, explaining the concepts above.