The concept you're referring to is known as "cosmic distance ladder" or "lookback time." It relates to the fact that light takes time to travel through space. When we observe distant objects in the universe, we are actually seeing them as they were in the past because the light emitted from those objects takes time to reach us.
In the context of stars, when we observe a star that is, let's say, 100 light-years away, we are seeing the light that the star emitted 100 years ago. This means that we are effectively looking back in time and observing the star as it was 100 years ago.
The same principle applies to more distant stars and galaxies. For example, if we observe a galaxy that is a billion light-years away, we are seeing the galaxy as it appeared a billion years ago.
So, when we say that some stars look older than others, it simply means that we are observing them as they appeared at an earlier point in their existence. The age of a star is determined by various factors such as its mass, composition, and evolutionary stage, but the perceived age can also be affected by the distance from which we observe it.
It's important to note that the Big Bang itself did not mark the starting point for individual stars. Stars formed billions of years after the Big Bang through processes of stellar birth and evolution. The age of a star is measured from its formation, but our observation of a star's light can be delayed due to the finite speed of light.
In summary, the perception of some stars appearing older than others is a result of observing them as they were in the past due to the time it takes for light to travel across vast cosmic distances.