Light of the World
One of the most difficult moments in high school comes when you encounter the word "trigonometry." It seems horribly abstract and useless, full of theorems to prove with no value whatever. But seen from the light of later years, it appears the universe runs on sines and cosines—with an occasional tangent thrown in.
Mathematics, especially the more abstract variety, tends to divide the world into those who understand and therefore see the use of it, and those who don't—and don't.
Jesus Christ is like that. Those who know him, those who love him, see no difficulty at all in calling him the light of the world. It is obvious that he is. Those who don't know him can't understand what this phrase might mean. So let us look at the light of the world in ways clear to those who love him:
To say that Jesus is the light of the world is to say that in him is found the full brilliance of God the Father. The Bible assures us that he is the "exact representation" of God, and that includes the glory of God.
Light—which cannot be impure
Any material object can be made dirty; just ask the mother of a toddler. But light cannot; it is therefore the symbol of purity. In this sense we see in the light of the world the holiness of God.
Sometimes, no matter how familiar you are with the house, you have to turn on a light to find something—or avoid stumbling over it. When you have the light, things become clear which otherwise remain darkened. Jesus is like that; with him the things of God become clear. Otherwise, they remain a mystery.
Light of life
Jesus explicitly tells us he is the light of life—which tells us that, as light itself can only be changed or absorbed, never destroyed, that the life in him is eternal.
There is one other thing we must note. He is "the" light of the world. God the Father, holiness, revelation and life can be found in no one else. It is fashionable today to say, "all religions are equally true." Which means they are equally false. Truth does not carry this characteristic; it is a single valued function, as the mathematicians might say. Come to the Light of the World, and you will indeed see.