14 You are the light of the world. A city set on a hill cannot be hid.
15 Nor do men light a lamp and put it under a peck-measure but on a lamp stand, and it gives light to all in the house.
16 Let your light so shine before men that they may see your moral excellence and your praiseworthy, noble and good deeds, and recognize and honor and praise and glorify your Father Who is in heaven.
13 In this verse and v.14, "You" is emphatic-"You, my followers and none others, are the salt of the earth." Salt was used in the ancient world to flavor foods and even in small doses as fertilizer. Above all, salt was used as a preservative. Rubbed into meat, a little salt would slow decay. Strictly speaking salt cannot lose its saltiness; sodium chloride is a stable compound. But most salt in the ancient world derived from salt marshes rather than evaporation of salt water, and thus contaminated many impurities. The actual salt, being more soluble than the impurities, could be leached out, leaving a residue so dilute it was of little worth.
The question "How can it be made salty again?" is not meant to have an answer. The point is that if Jesus' disciples are to act as a preservative in the world by conforming to kingdom norms, they can discharge this function only by retaining their own virtue.
14-15 Though the Jews saw themselves as the light of the world (Rom 2:19), the true light is the Suffering Servant (Isa 42:6; 49:6), fulfilled in Jesus himself (Matt 4:16; cf. Jn 8:12; 1 Jn 1:7). Derivatively his disciples constitute the new light (cf. Eph 5:8-9; Php 2:15). In the OT as in the NT, light most frequently symbolizes purity as opposed to filth, truth as opposed to error, knowledge as opposed to ignorance, and divine revelation and presence as opposed to reprobation and abandonment by God.
The reference to the "city on a hill" is at one level fairly obvious. Often built of white limestone, ancient towns gleamed in the sun and could not easily be hidden. At night the inhabitants' oil lamps would shed some glow over the surrounding area. As such cities could not be hidden, so also it is unthinkable to light a lamp and hide it under a peck-measure. A lamp is put on a lampstand to illuminate all. The "city on a hill" saying may also refer to OT prophecies about the time when Jerusalem or the mountain of the Lord's house would be lifted up before the world and the nations would stream to it (e.g., Isa 2:2-5). Jesus' disciples constitute the true locus of the people of God and the means of witness to the world.
16 Jesus drives the metaphor home. His disciples must show their "good works"-i.e., all righteousness, everything they are and do that reflects the mind and will of God. And others must see this light. It may provoke persecution (vv. 10-12), but that is no reason for hiding the light by which others may come to glorify the Father. Witness includes not just words but deeds as well.
Thus the kingdom norms (vv.3-12) so work out in the lives of the kingdom's heirs as to produce the kingdom witness (vv.13-16). If salt (v.13) exercises the negative function of delaying decay and warns disciples of the danger of compromise and conformity to the world, then light (vv.14-16) speaks positively of illuminating a sin-darkened world and warns against a withdrawal from the world that does not lead others to glorify the Father in heaven.
[NIV BIBLE COMMENTARY Volume 2: New Testament].
JESUS IS LORD.