In Acts 15, around the year AD 50, the remaining apostles of Jesus Christ were confronted by a conflict between the Jewish Christians and the Gentiles who were being converted to Christianity in growing numbers. The Jewish Christians in Antioch held that the Gentiles had to be circumcised in order to be saved, that belief in the death and resurrection of Christ wasn't enough.
Paul and his travelling companion Barnabas disagreed, and returned to Jerusalem to meet with the other apostles and leaders of the early Christian movement. This meeting was what was later known as the Jerusalem Council. Input and arguments were heard on all sides, with the loudest arguments for the following of Jewish law heard from the Pharisees.
Eventually Peter stood and addressed the council regarding the vision he had had in Acts 11, convincing him that Jesus had declared the Gentiles "clean" under the Jewish law by the blessing of the Holy Spirit. He ends: "We believe it is through the grace of our Lord Jesus that we are saved, just as they are." (Acts 15:11 NIV)
After some more words by Paul and Barnabas, James the brother of Jesus suggested that they should make it as easy as possible for the Gentiles to become part of the Christian brotherhood. He argued that they should not be forced to follow Jewish laws and traditions which neither they nor their cultures had ever followed. In a letter to the Gentiles, the Council agreed to recommend the following four laws only: "You are to abstain from food sacrificed to idols, from blood, from the meat of strangled animals and from sexual immorality" (Acts 15:29 NIV -- in other translations, "sexual immorality" is replaced with "fornication" or "unchastity"). Paul and Barnabas carried the letter back to Antioch, where it was received gladly.
Together with Acts 11, the decision of the Jerusalem Council formed the Biblical foundation for nearly every Christian church and denomination in the world today. They are the reason Christians do not follow the Levitical laws regarding clean or unclean food animals, marriage, justice, clothing, and so forth. The only laws which they are advised ("You will do well to avoid these things", v. 29) to follow are those summarized from Leviticus 17-18: Don't eat food offered to other "gods". Don't eat the blood of any animal or meat of a strangled animal, which still contains the blood. And don't violate the sexual purity of marriage.
Why does this short list remain? It was already understood by Gentile and Jewish Christians alike that belief in and baptism through Jesus as the resurrected Christ was essential to salvation. The goal of the Jerusalem Council was to strike a compromise between the Jewish and Gentile Christians on what else was expected, and it was probably believed that these laws were the minimal list that Jews would be willing to compromise on. None of them required a radical alteration of a Gentile Christian's lifestyle (although the call for sexual purity would probably strain the willpower of Christians then just as it does today). The fact that Luke records a favorable agreement on both sides in Acts 15 attests that the Council was held fairly and openly, and that the compromise was a true and good one.
It's also notable that the Council became the first of innumerable meetings among Christian church elders to decide church policy, meetings that would continue throughout history to the present day. Before, the Jews had the extensive Mosaic law in the Torah, along with the "traditions of the elders", to tell them what God did and did not require of them. Now that non-Jewish Christians were outnumbering Jewish ones, and since the Gospels had not yet been written or canonized, only the apostles' memories of Jesus' message and the wisdom bestowed upon them by the Holy Spirit at the Pentecost remained.
The letter of the Jerusalem Council was not held up as a "Four Commandments" for the Christian church, nor was it meant to be. The letter was phrased as only a strong advisement, to allow Gentile Christians to be accepted by their Jewish brothers. The basic principle of Christianity, while unspoken in the letter, still remained: "Believe in the Lord Jesus, and you will be saved." (Acts 16:31)