What symbolic meaning is conveyed through the stained glass in gothic cathedrals and byzantine art's opulent use of gold leaf and mosaic decoration?

Generally, the vitrage, or stained glass technique was used to convey an idea of other worldliness. When a person would enter the cathedral, the light would shine through the windows and illuminate the interior, causing a colourful ambient that would leave the person feeling as though they had entered another world; the world of God. The principle in the Byzantine age was the same, except it was more so to signify the god like attributes of the rulers themselves.