Although the complete light of the world parable is found only in Matthew 5, parts of it are found in Luke 8:16 and 11:33. It was given by Jesus near the start of his famous Sermon on the Mount. The sermon, offered shortly after Pentecost in 27 A.D., was likely spoken on Mount Eremos.
Following his teaching on being the salt of the earth (Matthew 5:13), Jesus' teachings encouraging Christians to let their light shine for all to see are the following.
You are the light of the world. A city that is set on a mountain cannot be hid.
Neither do they light a lamp and put it under a bushel basket, but on the lampstand; and it shines for all who are in the house. In the same way also, you are to let your light shine before men, so that they may see your good works, and may glorify your Father Who is in heaven (Matthew 5:14 - 16, HBFV).
What Makes It Possible
What makes it possible for Christians to be a shining advertisement for God?
Those who believe in and pursue behaving like Jesus become bearers of his light (Isaiah 9:1 - 2, Luke 2:32, John 1:4 - 12, 8:12) through God's Spirit in them. This spirit empowers Christians to understand the truth (John 16:13) and makes it possible for them to be spotlights pointing others to God the Father.
For you are all children of the light and children of the day; we are not of the night, nor of the darkness (1Thessalonians 5:5, see also Ephesians 5:8, HBFV throughout).
Jesus appeals to human experiences and common sense in this parable. A city, for example, placed on a hill cannot be hidden. At night, its light shines in the darkness, revealing its existence to those near and far and acting as a beacon to those in need.
The Lord further points out it would entirely defeat the purpose of a lamp or candle if they were placed under a bushel basket. These objects are made to be conspicuously placed so that they can illuminate as large an area as possible and benefit the most people.
Christians, called to be lights, do have a choice regarding how they shine in the world. They can choose to do good works privately where few if any are aware of their actions. There are no doubt many times when such behavior is warranted or even unavoidable (see John 21:25). That said, however, we should strive to do acts of charity that can be publically noticed where potentially many people can thank God for inspiring such service.
A Subtle Assertion
Jesus' subtle assertion is that faith in him, making us a light of the world, is intrinsically linked to good works. This fact is reiterated by the Apostle Paul.
For we are His workmanship, being created in Christ Jesus unto the good works that God ordained beforehand in order that we might walk in them (Ephesians 2:10, see also 1Timothy 6:18, 2Timothy 3:17).
The living faith necessary for our salvation should lead us to do as many good deeds as we can. Faith without these works is DEAD and those who think otherwise believe a lie (James 2:14 - 20).
Christians, like both salt and light, are meant to make a noticeable impact in the world. Our hearts should be set on doing good works for their own sake as an integral part of the righteous character developing in us (Matthew 5:48, John 17:23).
We should be mindful, however, not to do deeds to feed our vanity or for other selfish reasons. Jesus roundly condemned the Pharisees for performing works so that they could be seen and rewarded by others (Matthew 6:1 - 3, 23:5 - 7).
Whether it's donating time to a local foodbank, clearing a disabled neighbor's snow or helping the elderly, our selfless works should be noticeable to others. When we follow Jesus' words to "let your light shine before men" we bring glory and honor to God and His way of life.