What do we mean by the lookback time to a distant galaxy?
Due to the finite speed at which light travels, the light that reaches us from distant objects was emitted long ago and is very old when it finally brings information to Earth.
Because light travels at a finite velocity (
So, if a star were to be one light year away from us, light from that star, upon reaching us, has been travelling through space for one year. When we collect that light (we see the star) we are gathering light that has was emitted one year ago. We see the star not as it is at this moment, but as it was one year ago.
If you extend this fact to much greater distances, we realize that the further the object is from the Earth, the "older" the light that we gather when we look at that object. For example, Andromedia I galaxy is 2.43 million light years from us. So, the galaxy we see today is based on light emitted 2.43 million years ago. And for more distant objects, the light is even more ancient.
In that way, a look into the depths of the universe is a look back in time.
By the way, it is interesting to note that inhabitants of Earth have only been broadcasting electromagnetic signal for roughly a century. So, that information about us has only had time to travel about 100 light years. Other than our own Milky Way galaxy, there are very few objects "out there" within a 100 light year radius. Any alien life receiving a signal from us would have to be very close indeed!