While the story of Jesus healing a leper seems very simple, there was a lot more to its significance than you may think. Please read the account which only takes four verses in the Book of Matthew. The same account is further expounded upon by Mark with more detail. After reading these two accounts, then read the commentary from the James Talmage book Jesus the Christ.
As I read this story, I always recall the detail that according to the Law of Moses, if a man touches a leper, he is cast out of the city for a period of time. Jesus showed compassion and love. He touched the leper. Think about that when you are dealing with people who are outcasts of whatever social circles you live in.
Matthew 8 : 1-4 KJV
1. When he was come down from the mountain, great multitudes followed him.
2. And, behold, there came a leper and worshipped him, saying, Lord, if thou wilt, thou canst make me clean.
3. And Jesus put forth his hand, and touched him, saying, I will; be thou clean. And immediately his leprosy was cleansed.
4. And Jesus saith unto him, See thou tell no man; but go thy way, shew thyself to the priest, and offer the gift that Moses commanded, for a testimony unto them.
Mark 1 : 38-45 KJV
38. And he said unto them, Let us go into the next towns, that I may preach there also: for therefore came I forth.
39. And he preached in their synagogues throughout Galilee, and cast out devils.
40. And there came a leper to him, beseeching him, and kneeling down to him, and saying unto him, If thou wilt, thou canst make me clean.
41. And Jesus, moved with compassion, put forth his hand, and touched him, and saith unto him, I will; be thou clean.
42. And as soon as he had spoken, immediately the leprosy departed from him, and he was cleansed.
43. And he straitly charged him, and forthwith sent him away;
44. And saith unto him, See thou say nothing to any many: but go thy way, shew thyself to the priest, and offer for thy cleansing those things which Moses commanded, for a testimony unto them.
45. But he went out, and began to publish it much, and to blaze abroad the matter, insomuch that Jesus could no more openly enter into the city, but was without in desert places: and they came to him from every quarter.
Jesus the Christ
Written by James Talmage
CONTINUATION OF OUR LORD’S MINISTRY IN GALILEE.
A LEPER MADE CLEAN.
Early in the morning following that eventful Sabbath in Capernaum, our Lord arose “a great while before day” and went in quest of seclusion beyond the town. In a solitary place He gave Himself to prayer, thus demonstrating the fact that, Messiah though He was, He was profoundly conscious of His dependence upon the Father, whose work He had come to do. Simon Peter and other disciples found the place of His retirement, and told Him of the eager crowds who sought Him. Soon the people gathered about Him, and urged that He remain with them; but “he said unto them, I must preach the kingdom of God to other cities also: for therefore am I sent.”  And to the disciples He said: “Let us go into the next towns, that I may preach there also: for therefore came I forth.” Thence He departed, accompanied by the few whom He had already closely associated with Himself, and ministered in many towns of Galilee, preaching in the synagogs, healing the sick, and casting out devils.
Among the afflicted seeking the aid that He alone could give came a leper, who knelt before Him, or bowed with his face to the ground, and humbly professed his faith, saying: “If thou wilt, thou canst make me clean.” The petition implied in the words of this poor creature was pathetic; the confidence he expressed is inspiring. The question in his mind was not—Can Jesus heal me? but—Will He heal me? In compassionate mercy Jesus laid His hand upon the sufferer, unclean though he was, both ceremonially and physically, for leprosy is a loathsome affliction, and we know that this man was far advanced in the disease since we are told that he was “full of leprosy.” Then the Lord said: “I will: be thou clean.” The leper was immediately healed. Jesus instructed him to show himself to the priest, and make the offerings prescribed in the law of Moses for such cases as his. 
In this instruction we see that Christ had not come to destroy the law, but, as He affirmed at another time, to fulfil it; and at this stage of His work the fulfilment was incomplete. Moreover, had the legal requirements been disregarded in as serious a matter as that of restoring an outcast leper to the society of the community from which he had been debarred, priestly opposition, already waxing strong and threatening against Jesus, would have been augmented, and further hindrance to the Lord’s work might have resulted. There was to be no delay in the man’s compliance with the Master’s instruction; Jesus “straitly charged him, and forthwith sent him away.” Furthermore He explicitly directed the man to tell nobody of the manner of his healing. There was perhaps good reason for this injunction of silence, aside from the very general course of our Lord in discountenancing undesirable notoriety; for, had word of the miracle preceded the man’s appearing before the priest, obstacles might have been thrown in the way of his Levitical recognition as one who was clean. The man, however, could not keep the good word to himself, but went about “and began to publish it much, and to blaze abroad the matter, insomuch that Jesus could no more openly enter into the city, but was without in desert places: and they came to him from every quarter.”
 Luke 4:42-44.
 Mark 1:38.
 Mark 1:40-45; Matt. 8:2-4; Luke 5:12-15.
 Leprosy.—In Biblical usage this name is applied to several diseases, all, however having some symptoms in common, at least in the earlier stages of the malady. The real leprosy is a scourge and a plague in many oriental lands to-day. Zenos, in Standard Bible Dict., says: “True leprosy, as known in modern times, is an affection characterized by the appearance of nodules in the eye-brows, the cheeks, the nose, and the lobes of the ears, also in the hands and feet, where the disease eats into the joints, causing the falling off of fingers and toes. If nodules do not appear, their place is taken by spots of blanched or discolored skin (Mascular leprosy). Both forms are based upon a functional degeneration of the nerves of the skin. Its cause was discovered by Hansen in 1871 to be a specific bacillus. Defective diet, however, seems to serve as a favorable condition for the culture of the bacillus. Leprosy was one of the few abnormal conditions of the body which the Levitical law declared unclean. Elaborate provision was therefore made for testing its existence and for the purification of those who were cured of it.”
Deems, Light of the Nations, p. 185, summing up the conditions incident to the advanced stages of the dread disease, writes: “The symptoms and the effects of this disease are very loathsome. There comes a white swelling or scab, with a change of the color of the hair on the part from its natural hue to yellow; then the appearance of a taint going deeper than the skin, or raw flesh appearing in the swelling. Then it spreads and attacks the cartilaginous portions of the body. The nails loosen and drop off, the gums are absorbed, and the teeth decay and fall out; the breath is a stench, the nose decays; fingers, hands, feet, may be lost, or the eyes eaten out. The human beauty has gone into corruption, and the patient feels that he is being eaten as by a fiend, who consumes him slowly in a long remorseless meal that will not end until he be destroyed. He is shut out from his fellows. As they approach he must cry, ‘Unclean! unclean!’ that all humanity may be warned from his precincts. He must abandon wife and child. He must go to live with other lepers, in disheartening view of miseries similar to his own. He must dwell in dismantled houses or in the tombs. He is, as Trench says, a dreadful parable of death. By the laws of Moses (Lev. 13:45; Numb. 6:9; Ezek. 24:17) he was compelled, as if he were mourning for his own decease, to bear about him the emblems of death, the rent garments; he was to keep his head bare and his lip covered, as was the custom with those who were in communion with the dead. When the Crusaders brought the leprosy from the East, it was usual to clothe the leper in a shroud, and to say for him the masses for the dead…. In all ages this indescribably horrible malady has been considered incurable. The Jews believed that it was inflicted by Jehovah directly, as a punishment for some extraordinary perversity or some transcendent act of sinfulness, and that only God could heal it. When Naaman was cured, and his flesh came back like that of a little child, he said, ‘Now I know that there is no God in all the earth but in Israel,’ (2 Kings 5:14, 15.)”
The fact that leprosy is not ordinarily communicable by mere outward contact is accentuated by Trench, Notes on the Miracles, pp. 165-168, and the isolation of lepers required by the Mosaic law is regarded by him as an intended object lesson and figure to illustrate spiritual uncleanness. He says: “I refer to the mistaken assumption that leprosy was catching from one person to another; and that the lepers were so carefully secluded from their fellowmen lest they might communicate the disease to others, as in like manner that the torn garment, the covered lip, the cry, ‘Unclean, unclean’ (Lev. 13:45) were warnings to all that they should keep aloof, lest unawares touching a leper, or drawing unto too great a nearness, they should become partakers of this disease. So far from any danger of the kind existing, nearly all who have looked closest into the matter agree that the sickness was incommunicable by ordinary contact from one person to another. A leper might transmit it to his children, or the mother of a leper’s children might take it from him; but it was by no ordinary contact communicable from one person to another. All the notices in the Old Testament, as well as in other Jewish books, confirm the statement that we have here something very much higher than a mere sanitary regulation. Thus, when the law of Moses was not observed, no such exclusion necessarily found place; Naaman the leper commanded the armies of Syria (2 Kings 5:1); Gehazi, with his leprosy that never should be cleansed, (2 Kings 5:27) talked familiarly with the king of apostate Israel (2 Kings 8:5)…. How, moreover, should the Levitical priests, had the disease been this creeping infection, have ever themselves escaped it, obliged as they were by their very office to submit the leper to actual handling and closest examination?… Leprosy was nothing short of a living death, a corrupting of all the humors, a poisoning of the very springs, of life; a dissolution, little by little, of the whole body, so that one limb after another actually decayed and fell away. Aaron exactly describes the appearance which the leper presented to the eyes of the beholders, when, pleading for Miriam, he says, ‘Let her not be as one dead, of whom the flesh is half consumed when he cometh out of his mother’s womb.’ (Numb. 12:12.) The disease, moreover, was incurable by the art and skill of man; not that the leper might not return to health; for, however rare, such cases are contemplated in the Levitical law…. The leper, thus fearfully bearing about the body the outward and visible tokens of sin in the soul, was treated throughout as a sinner, as one in whom sin had reached its climax, as one dead in trespasses and sins. He was himself a dreadful parable of death. He bore about him the emblems of death (Lev. 13:45); the rent garments, mourning for himself as one dead; the head bare as they were wont to have it who were defiled by communion with the dead (Numb. 6:9; Ezek. 24:27); and the lip covered (Ezek. 24:17)…. But the leper was as one dead, and as such was shut out of the camp (Lev. 13:46; Numb. 5:2-4). and the city (2 Kings 7:3), this law being so strictly enforced that even the sister of Moses might not be exempted from it (Numb. 12:14, 15); and kings themselves, as Uzziah (2 Chron. 26:21; 2 Kings 15:5) must submit to it; men being by this exclusion taught that what here took place in a figure, should take place in the reality with every one who was found in the death of sin.”
For the elaborate ceremonies incident to the cleansing of a recovered leper see Lev. chap. 14.
 Matt. 5:17.
 Mark 1:45.