Their character was described in the previous verses, and are those who put their faith in the Lord Jesus.
By "salt of the Earth”, it is meant that their character is beneficial for the population of the Earth. Salt is known for its properties to sanitize and preserve that on which it is applied. Those who seek to live righteously, honestly, fairly, in obedience to the principles of the Kingdom of Christ, have a positive influence on the environment in which they live.
Nevertheless, the effectiveness of salt depends on its quality. Only because something is called “salt" we cannot be sure that it is good for salting... So, too, just calling ourselves "Christians" does not cause us to have any influence for good in the world if not accompanied by good works resulting from the character of a disciple of Christ.
Darkness in reality is nothing more than the absence of light. You cannot impose darkness over light, but light, no matter how small, is always seen in the darkness. For a light not to be seen, it must be covered.
The Lord Jesus declared Himself the light of the world while He was in the world (John 9:5), and here He declares that the disciples are the light of the world, no doubt reflecting His light after His Ascension. The believer shines for the Lord Jesus, having in himself the light of the Gospel, of which he bears witness to those around him.
As a city built on a hill cannot be hidden, also the believer cannot help but reveal himself by his conduct: his sanctified life contrasts with the behaviour of unbelievers.
The lampstand is a small device, made of tinplate or clay, stocked with oil and with a wick, used on a disk that sits on top of a wooden rod propped on a base on top of a wall. The bushel (or basket) is a square container, usually made of wood and with two wings, used to measure a bushel of grain. Nobody covers the lamp on the floor with the bushel, for it would then be useless, but on the lampstand to light up the house.
The believer cannot hide his light, but should radiate the light of Christ’s teaching, the Gospel, through his behaviour and witness to those who are around him. The purpose of this is not to gain thanks and praise for himself, but as people see his good works, they will glorify our Father in heaven. The purity of the lives in which Christ is seen speaks louder than the persuasion of words.
The Lord Jesus declares that He did not come to abolish the law or the prophets. He was not a revolutionary, cutting all ties with the past and introducing a new religion. Instead, he came to fulfil the Law of Moses, and the prophecies about him in the Old Testament.
He insisted that none of the smallest details of the law would be left unfulfilled. No sin was found in His Person. Furthermore, a good part of the Law of Moses involved sacrifices, rituals and formalities: all were figures of the Messiah who was to come, and they were all fulfilled in Jesus Christ.
The prophecies about His birth and His role as the Lamb of God, sacrificed for the sins of the world were also fulfilled. The remaining prophecies about the triumphant Messiah, which delivers the remnant of Israel from their enemies and establishes His Kingdom on Earth, will also be fulfilled faithfully when the Day of the Lord comes. The new heavens and the new Earth will come later.
Jesus Christ having fulfilled all the Law, it ceases to have relevance in its ceremonial aspect, which includes the priesthood, the sacrifices and the sanctified days. He is the priest and the sacrifice. Those who receive Christ as their Lord and Saviour "die" to the law by the body of Christ, which was sacrificed in their stead (Romans 7:4), and the law was not made for them (1 Timothy 1: 9).
However, the Law of Moses still stands for unbelievers, as it is by law that their sins are evidenced, so convincing them of the need for repentance and forgiveness that can only be achieved through faith in the Saviour, Jesus Christ.
Believers in Christ belong to the Kingdom of God, having been freed from the observance of the Law of Moses to instead serve Christ and bear fruit for God.
The Kingdom of God has its law, the law of the Messiah (1 Corinthians 9:21), somewhat more demanding than the law of Moses, and that boils down to love others as yourself and not do harm to a neighbour (Romans 13: 8-10).
The Lord Jesus clarifies that “whoever breaks one of the least of these commandments, and teaches men so, shall be called least in the kingdom of heaven; but whoever does and teaches them, he shall be called great in the kingdom of heaven". Let us note that there is no death penalty, because the believer does not lose his salvation, which is eternal, but his degree of obedience will have an effect on his position in the Kingdom.
Following this, we find several aspects of the law of the Kingdom of the Messiah, with more details explained in other parts of the New Testament. They are given, as all Scripture, “for doctrine, for reproof, for correction, for instruction in righteousness” (2 Timothy 3:16). Only nine of the Ten Commandments are repeated, because keeping of the Sabbath is not required from believers.
To enter the Kingdom of Heaven requires a degree of righteousness exceeding that of the scribes and Pharisees: it is by being justified by faith in Christ.
Then the Lord Jesus shows us some ways in which the law of His Kingdom is even more comprehensive than the one given through Moses:
It had been said: you shall not murder: of equal severity (danger of judgment) is being angry against a brother without cause (seed of murder), even worse is to insult him (spirit of murder), and worst of all is to curse him (desire to murder). Who offends another person must first reconcile with him before bringing his offering to God.
It had been said: you shall not commit adultery: the law condemns the physical act, but adultery is already carried out when looking upon a woman to lust after her. Sin begins in the mind, and for the thoughts to remain pure, a severe discipline is required, comparing to blinding an eye or cutting off a hand.
It had been said: the husband may leave his wife, giving her a letter of divorce: the husband who repudiates his wife, except for sexual impurity (not adultery, for she would be stoned), causes her to tamper with another man, and he will be committing adultery if he marries her. It is implied that the charge of sin falls on the first husband, who will be blamed for the subsequent sins.
It had been said: you shall not swear falsely, but shall perform your oaths to the Lord: it is wrong to swear by Heaven, Earth, and Jerusalem or by one’s own head because we have no authority over them, making it possible to commit a perjury. We should not give more than our word (and never lie, because it is a sin).
It had been said: An eye for an eye, and a tooth for a tooth: we must not revenge ourselves, but pay good for evil.
It had been said: You shall love your neighbour and hate your enemy: just as the love of God encompasses all, we too should love and to do good to all, even to our enemy.
The law gave a measure of righteousness only: we must go further and be perfect just as our Father in heaven is perfect. This perfection is the spiritual maturity that allows the believer to imitate God, blessing everyone without partiality.
13 "You are the salt of the earth; but if the salt loses its flavor, how shall it be seasoned? It is then good for nothing but to be thrown out and trampled underfoot by men.
14 "You are the light of the world. A city that is set on a hill cannot be hidden.
15 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.
16 Let your light so shine before men, that they may see your good works and glorify your Father in heaven.
17 "Do not think that I came to destroy the Law or the Prophets. I did not come to destroy but to fulfill.
18 For assuredly, I say to you, till heaven and earth pass away, one jot or one tittle will by no means pass from the law till all is fulfilled.
19 Whoever therefore breaks one of the least of these commandments, and teaches men so, shall be called least in the kingdom of heaven; but whoever does and teaches them, he shall be called great in the kingdom of heaven.
20 For I say to you, that unless your righteousness exceeds the righteousness of the scribes and Pharisees, you will by no means enter the kingdom of heaven.
21 "You have heard that it was said to those of old, 'YOU SHALL NOT MURDER, and whoever murders will be in danger of the judgment.'
22 But I say to you that whoever is angry with his brother without a cause shall be in danger of the judgment. And whoever says to his brother, 'Raca!' shall be in danger of the council. But whoever says, 'You fool!' shall be in danger of hell fire.
23 Therefore if you bring your gift to the altar, and there remember that your brother has something against you,
24 leave your gift there before the altar, and go your way. First be reconciled to your brother, and then come and offer your gift.
25 Agree with your adversary quickly, while you are on the way with him, lest your adversary deliver you to the judge, the judge hand you over to the officer, and you be thrown into prison.
26 Assuredly, I say to you, you will by no means get out of there till you have paid the last penny.
27 "You have heard that it was said to those of old, 'YOU SHALL NOT COMMIT ADULTERY.'
28 But I say to you that whoever looks at a woman to lust for her has already committed adultery with her in his heart.
29 If your right eye causes you to sin, pluck it out and cast it from you; for it is more profitable for you that one of your members perish, than for your whole body to be cast into hell.
30 And if your right hand causes you to sin, cut it off and cast it from you; for it is more profitable for you that one of your members perish, than for your whole body to be cast into hell.
31 "Furthermore it has been said, 'Whoever divorces his wife, let him give her a certificate of divorce.'
32 But I say to you that whoever divorces his wife for any reason except sexual immorality causes her to commit adultery; and whoever marries a woman who is divorced commits adultery.
33 "Again you have heard that it was said to those of old, 'You shall not swear falsely, but shall perform your oaths to the Lord.'
34 But I say to you, do not swear at all: neither by heaven, for it is God's throne;
35 nor by the earth, for it is His footstool; nor by Jerusalem, for it is the city of the great King.
36 Nor shall you swear by your head, because you cannot make one hair white or black.
37 But let your 'Yes' be 'Yes,' and your 'No,' 'No.' For whatever is more than these is from the evil one.
38 "You have heard that it was said, 'AN EYE FOR AN EYE AND A TOOTH FOR A TOOTH.'
39 But I tell you not to resist an evil person. But whoever slaps you on your right cheek, turn the other to him also.
40 If anyone wants to sue you and take away your tunic, let him have your cloak also.
41 And whoever compels you to go one mile, go with him two.
42 Give to him who asks you, and from him who wants to borrow from you do not turn away.
43 "You have heard that it was said, 'YOU SHALL LOVE YOUR NEIGHBOR and hate your enemy.'
44 But I say to you, love your enemies, bless those who curse you, do good to those who hate you, and pray for those who spitefully use you and persecute you,
45 that you may be sons of your Father in heaven; for He makes His sun rise on the evil and on the good, and sends rain on the just and on the unjust.
46 For if you love those who love you, what reward have you? Do not even the tax collectors do the same?
47 And if you greet your brethren only, what do you do more than others? Do not even the tax collectors do so?
48 Therefore you shall be perfect, just as your Father in heaven is perfect.
Matthew chapter 5, verses 13 to 48