One could draw a number of lessons from this narrative. Because this is Matthew's first extended healing miracle, I will treat some elements in greater detail here than in some subsequent narratives.
The Leper Does Not Beseech Cavalierly (8:1-2)
This leper was in a desperate and apparently lifelong situation. Biblical leprosy (distinct from modern Hansen's disease) was an assortment of serious skin problems that isolated the leper from the rest of society (Trapnell 1982:459). Sometimes we pray passively, almost unconcerned as to whether God hears a particular prayer or not; the leper did not have this luxury. For another expression of desperate faith, see comment on 9:20-21.
The Leper Approaches Jesus with Humility (8:2)
Bowing down before another person was a great act of respect for the other's dignity, especially for a Jewish person (as in Test. Ab. 3-4, 9, 16A). The leper not only shows physical signs of respect toward Jesus; he acknowledges that Jesus has the right to decide whether to grant the request. To acknowledge that God has the right to grant or refuse a request is not lack of faith (8:2; compare, for example, Gen 18:27, 30-32; 2 Sam 10:12; Dan 3:18); it is the ultimate act of dependence on God's compassion and takes great trust and commitment for a desperate person.
The Leper Has Perfect Trust in Jesus' Power (8:2)
He knows Jesus is able to make him clean if he wants to; he is not using if you are willing as a religious way of saying, "I doubt that you can, but I would be happy if you might do something for me anyway." Yet the text demonstrates, as has been already noted, that his trust in Jesus' power is not presumption either.
Jesus Not Only Heals but Touches the Untouchable (8:3)
Jewish law forbade touching lepers (Lev 5:3) and quarantined lepers from regular society (Lev 13:45-46); people avoided most contact with them (2 Kings 7:3; Jos. Ant. 9.74). Some ruled that the defilement of leprosy was one of the greatest defilements, for a leper could communicate it even by entering a house (m. Kelim 1:4). It is thus no small matter for Jesus to compassionately touch the man. Yet by touching Jesus does not actually undermine the law of Moses, but fulfills its purpose by providing cleansing (Mt 5:17-48; compare Lev 13:3, 8, 10, 13, 17).
Some Christians today would fear to touch a Christian brother or sister who, through blood transfusion, past lifestyle or a spouse's infidelity, was HIV-positive, even though HIV is less contagious than many people thought leprosy was. As often happens today, some people in antiquity constructed theological rationalizations for others' misfortune perhaps to escape from the fear that they too were vulnerable; hence some later teachers decided that leprosy was divine punishment (m. Seqalim 5:3; Lev. Rab. 17:3).
Jesus Wants to Make the Man Whole (8:3)
Verse 3 implies what is elsewhere explicit: Matthew views compassion as a primary motivation in Jesus' acts of healing (9:36). Even if in some cases God has some higher purpose in mind than an immediate answer to our request (as in 26:39, 42), he is never sadistic. Jesus demonstrated his feeling toward our infirmities by bearing them with us and for us (8:17) and by healing all who sought his help (8:16). Matthew hardly expects us to suppose that Jesus has lost any of his power (28:18) or compassion since the resurrection. Unfortunately, many of us Western Christians today feel more at home with the Enlightenment rationalism in which we were trained than we do with the desperate faith of Christians who dare to believe God for miracles. Those in desperate need cannot afford to rationalize away God's power and compassion.
Jesus Does Not Seek Human Honor for Himself (8:4)
This healing would be viewed as no small miracle; later Jewish teachers regarded leprosy as akin to death (compare Num 12:12; 2 Kings 5:7) and cleansing a leper as akin to raising the dead (b. Sanhedrin 47a). Yet not only does Jesus refuse to take advantage of the opportunity for publicity, he attempts to suppress it. Some other prominent biblical prophets at times worked clandestinely, endeavoring to accomplish their mission without seeking their own honor (for example, 1 Kings 11:29; 13:8-9; 21:18; 2 Kings 9:1-10), partly because they were investing their time especially in a small circle of disciples (1 Sam 19:20; 2 Kings 4:38; 6:1-3; Keener 1993:134). There are also other important reasons for the messianic secret, but whatever the other reasons, Jesus is not interested in getting credit from others for everything he does (compare Mt 6:1-18).
Jesus Honors the Requirements of the Law of Moses (8:4)
Jesus upholds the law (Mt 5:17-20): the law commanded lepers who thought they were cleansed to submit to priestly inspection and offer sacrifice (Lev 14:1-9; CD 13.6-7; m. Nega`im). Jesus may not seek credit for the miracle, but his faithfulness to the law takes precedence over his personal prohibition against announcing the work.