We all know that light travels really fast. It can appear instantaneous to us on earth, but when you look out into space, you are looking at objects in the past because the light from that object has not yet reached us. If the sun just vanished, we would not know it for 8 minutes because the light takes that long to reach us. One way to look at this effect is through light cones.
The point of the light cone is the object you are looking at. The object it affects starts at the same point in time (or at the same horizontal position). As the objects move forward in time they move upward through the cone. The cone represents the light’s range as it spreads out. So you can see when objects will finally be affected by the object causing the light cone. As in this diagram, you can see how earth doesn’t intersect the future light cone of the Sun for 8 minutes, so we wouldn’t notice a change in the Sun for 8 minutes.
Another cool thing to look at is past light cones. You can see what events can affect an object, such as the Earth, at the present moment. Since nothing can travel faster than light, the event affecting Earth must be located inside the past light cone. If it were outside, then the light leaving the event must be traveling faster than the speed of light in order to get to us at the present, which is impossible. While they can be complicated, light cones are a very helpful way to view how the speed of light acts in relation to space-time and a cool representation of how light spreads out over time.
A Brief History of Time, by Steven Hawking