Bella, great question! You're obviously reading or listening to some intriguing material and thinking very deeply about it. Here's the scoop...
Let's say that one of our super-high-powered telescopes sees a star "being born" in some distant corner of the universe. The star that is being seen here could actually be very, very old... or, it could even be DEAD! But we're able to see its birth! How is this?
Our observation of the star depends upon LIGHT (whether that's red, orange, yellow, green, blue, indigo, violet LIGHT, x-ray LIGHT, microwave LIGHT, or any other kind of LIGHT). Light takes time to get anywhere. I've heard that we are able to "see" things out to 40 or 50 billion light years away. That means that if a star is (or was) 40 billion light years away, we are NOW seeing the light that it gave off 40 billion years ago. If a planet is that far away, then we are NOW seeing the light that illuminated that planet (and reflected off of it) 40 billion years ago.
Obviously, a lot can happen in 40 billion years. Maybe 30 billion years ago, that star disappeared. If we're just seeing its birth now, then we'll continue to see that star for another 10 billion years. You see, for the next 10 billion years, we'll be collecting the light that the star once gave off.
Does this make sense?
Here's another way to think about it: Throw a stone into a pond. How do you know that the stone hit the water? You see it, duh. But what if we couldn't "see" it? You could stick your fingers into the calm edge of the pond and wait until you felt the ripples. Just because you feel the ripples doesn't mean that the stone is JUST THEN hitting the surface. Nope, the stone is already long-gone. You're just collecting the PAST information now.
So, we're "seeing into the past," because of the speed of light. Light's fast, but it's not instantaneous. It takes time to get from point A to point B. In the time that it takes to cross the universe, a lot can happen. Stars are born and die. Galaxies are formed. Planets are formed.
Let's say that earth is about 4.6 billion years old. Maybe there's another planet kind of like ours (same age and approximate size). If that planet happened to be 4.6 billion light years away, we could watch its birth even though that all happened a long, long time ago. Even though our planet may have had a very different birth, we could get an idea as to what was happening to other planets at that time in the universe.
Finally, keep in mind that even though we've got this "gift" of seeing into the past, we are very, very blind as to what is happening NOW. Since light is the fastest means of observing things, there is absolutely no way to know what is happening NOW with that star that is/was 40 billion light years away. We're watching its past, but that's all we can do - just watch it unfold gradually before our eyes. Fascinating universe that we've been blessed with, no?