How can people literally see the past by using light waves?

Here's the example that illustrate what you just asked. I will be using this example from astronomy. When you look up the sky to the stars, you are literally seeing into the past. The distance from you to the star you are looking at is x lightyears away. Lightyear is distance light travles in 1 year. So if a star is, say 100 lightyears away from you, then you are seeing the state of the star that much time ago.