Many objects that astronomers study are so far away that they cannot be resolved in telescopes. They appear only as points in images. Astronomers are thus faced with a difficulty in determining their physical size: indirect means must be used to derive the size of these unresolved objects.
One method used by astronomers to estimate the size of an object is to note how rapidly it varies in brightness. The method is not extremely accurate, but it does give an upper limit, or a maximum size for a given object. The reason for this can be understood by considering the finite speed of light and simple geometry.
We can imagine some astronomical source that emits radiation from some region in space. We will assume the region has some unknown extent, and that the amount of radiation from the object all increases instantaneously.
As we view the object, we will see the light from its near side arrive at some time; call it t1. However, the light from its far side has an extra distance to cover, so it will arrive a little bit later, at a time t2. The difference in these two arrival times will be due (under these simple assumptions) only to the different distances traveled by the light from the near and far side, and this distance is d = c(t2 − t1), and we will see the brightness of the object constantly increase over this time.
Of course, it could also be the case that different parts of the object brightened at different times, so the time delay could be caused by physical processes going on within the source. For this reason this time delay method is not a reliable way to determine the size of an object. It only tells us that the object cannot be any larger than the light travel time would suggest, but it could certainly be smaller if different parts brightened at different times.
It should be clear that the same arguments would apply if the object became dimmer instead of brighter. Any change in brightness can give us an idea of how large the source of radiation could be.