Matthew 5.14-16:
You are the light of the world. A city set on a hill cannot be hidden. (15) Nor do people light a lamp and put it under a basket, but on a stand, and it gives light to all in the house. (16) In the same way, let your light shine before others, so that they may see your good works and give glory to your Father who is in heaven. (ESV)
The verses above are a part of the teaching of Jesus known as the Sermon on the Mount. Jesus had been teaching in the synagogues in Galilee and healing the diseases of the people. This made Jesus famous in the area and large crowds were following him. When Jesus saw the crowds, he went up on a mountain and began teaching the crowd.
There are a number of approaches that have been taken in interpreting the Sermon on the Mount, because some of what Jesus taught seems so extreme, and it was strikingly different than what the teachers of the Law were teaching at this time. The above verses have their challenges.
In the Gospel of John it is clearly established that Jesus is the light of the world, both from the Prologue of the Gospel and from the words of Jesus himself in John 8.12. So for Jesus to say that his disciples are the light of the world, we must understand his statement in terms of being rightly related to Jesus, and how the light of Jesus gets lived out in our lives.
All people by their nature are sinful and incapable of satisfying God’s Law. We may not want to look at our human nature in this way, but if we examine ourselves honestly by the standard Jesus sets forth in the Sermon on the Mount and other teaching in the Bible, we must conclude this is true. The only person who has ever lived, with the light shining out from the nature of his own being, is Jesus. So for the followers of Jesus to be the light of the world themselves, they must have a definite, certain relationship with Jesus.