Prior to the Gospel of Luke 17:12-19 telling of the healing of the 10 lepers is a story of the healing of another leper in Luke 12:15 (Matthew 8:1-4; Mark 1:40-45). In both of these stories, Jesus instructs the people inflicted with leprosy to show the priests that they were healed. In the ancient world, leprosy was considered a disease that was the result of sin. The disease caused great suffering and it was contagious, therefore, the people afflicted with this disease were banished to live in areas remote to the general population. The priests would have had the power to release the leper from banishment so he could rejoin the community of believers as having been purified of their defilement.
The difference between the two stories about the lepers in Luke is that in the first story the leper was clearly a Jew and told to follow the command of Moses and make an offering for his cleaning, an offering of thanksgiving, after the priests had certified that he no longer had the disease. In the second story there was one Samaritan among the 10 lepers that were cured. They were all told by Jesus to go and show themselves to the priests, but Jesus did not tell them to make a thank offering as he did in the earlier story in Luke. The only person who personally thanked Jesus Himself for curing him was the Samaritan.
Actually, the Samaritan would not have gone to the same worship center as the other 9 Jewish lepers once they were healed. To clarify, the Samaritans worshiped the God of Israel and claimed their ancestry through the two Grandsons of Jacob by his son Joseph, Ephraim and Manasseh. Some biblical scholars include the tribes of Benjamin and Levi in the Samaritan ancestry as well. They accepted the first five books of the Old Testament that were written by Moses and were waiting for the Messiah. They considered themselves to hold the faith of the ancient Israelites in its original form before the Babylonian Exile, preserved unaltered by those who remained in the land of Israel. There is some evidence that their very name in the Samaritan Hebrew language is really ‘Samerim’, which means “Keepers/Guardians of the Law”. They were a mixed race of people and traditional enemies of the Jews. The major problem between the Jews and the Samaritans was the location of the place to worship God. According to the Jews, the place was Jerusalem. According to the Samaritans, the original place was Mount Gerizim because that is where the tribes of Israel settled after Joshua conquered Canaan (Deut. 11:29; 27:12; Josh. 8:33). This dispute in location of the Holy place to worship God was worsened when the Jews destroyed the temple of the Samaritans on Mount Gerizim in 128 BC.
Most biblical scholars conclude that the singling out of the Samaritan leper in this biblical story, and by extension those who would come to believe in the Lord’s Divinity who were Gentiles, is meant to convey that salvation from sin and death is offered by our Lord and God and Savior Jesus Christ to those who believe and offer glory to God for His great mercy offered to all mankind.
References: Josephus; Antiquities of the Jews: Josephus: the Wars of the Jews; Ancient Christian Commentary, IV-A; Fathers of the Church; The Gospel of Luke, Good News for the Poor by Lawrence Farley, Concilliar Press; The New Testament, Luke and Acts by Paul Nadim Tarazi, NKJV