Matthew 5:14,15 says - "You are the light of the world. A city that is set on a hill cannot be hidden. Nor do they light a lamp and put it under a basket, but on a lampstand, and it gives light to all who are in the house."
In addition to being "salt," Jesus' disciples are also "light"--namely, "the light of the world." The purpose of light is to enable people to see. Light provides: (1) illumination, (2) guidance, and (3) warning. Physical lights shine to dispel darkness, and in so doing serve as guides and warnings (e.g., headlights and lighthouses). Spiritual lights should function in the same manner. Psalm 119:105 reads - "Your word is a lamp to my feet and a light to my path." Consider also Proverbs 4:18,19 - "But the path of the just is like the shining sun, that shines brighter unto the perfect day. The way of the wicked is like darkness; they do not know what makes them stumble." God wants the world to see the truth, and our lights (lives) should reveal His truth (cf. John 8:12; Phil. 2:15). His truth should be clearly seen in our lives just as a city set on a hill is seen from all directions.
Think of the foolishness in lighting a lamp and then hiding its light. The purpose of lighting a lamp is to provide light for people to see. A major purpose in following Christ is to provide spiritual light for others to see. We must not hide under a "basket" for any reason, whether it is fear, indifference, love of the world, misplaced priorities, etc. Truly, one cannot be a secret disciple of Christ--either the secrecy will destroy the discipleship or the discipleship will destroy the secrecy. If one lights a lamp and puts it under a basket, either the basket will smother the flame and the light will go out (cf. Matt. 13:22) or the lamp will ignite the basket, burning it away for the light to be seen by all (cf. Jer. 20:9).
Our Lord commanded His followers in Matthew 5:16 - "Let your light so shine before men, that they may see your good works and glorify your Father in heaven."
For whom should we let our lights shine? The world! Why? That they might take notice of us and exalt us? No! That they might observe our good deeds and give glory and honor to the heavenly Father? Yes! Christians should desire that others see their good works in order to be drawn to God as a result. The good works we do should not all be secrets, otherwise we are hiding under a basket and not fulfilling our purpose as "light" for God.
Now please don't misunderstand. I believe there is a big difference between "shining your light" and "letting your light shine." The glory for good works is to go to the heavenly Father, not the individual! Yes, it is pleasing to God for men to see our good works, but only if we are not performing them to receive personal glory (cf. Matt. 6). In the same way, salt is not to draw attention to itself but emphasize the natural flavor of the food. Salt should not cover up or overpower the taste of food and neither should a light draw attention and honor to itself. After all, men do not praise the streetlights that protect them from thievery and assault, but they do praise the city administration which furnishes the lights! God is the giver of light and every perfect gift (James 1:17). We are nothing--except His servants. May we remember that and continually seek to direct praise to Him and not ourselves. To do such shows a thankful, humble spirit on our part. Such an attitude pleases God.
The primary idea of Matthew 5:13-16 is that Jesus' disciples should have a great positive influence on those they come in contact with. This influence will never materialize if Christians are content to hide in salt shakers or under baskets. You cannot be a secret disciple! Friends, be bold and courageous in fulfilling your duty to God and influencing others for good by your words and actions that give glory to Almighty God!