With the Gentiles now joining the church there was some "growing in unity" pains. The Jewish way of life and the Gentile way of life was now colliding and they need to come up with a solution, a statement that they could all unify around. This was a tough thing to do and required some humility on the part of the Jewish people. They had been following all these laws all these centuries to be the people of God and now these Gentiles show up and refuse some of the laws. They had to get together to sort this out.
The ones who had the toughest time accepting the Gentiles were the Pharisees. Their legalism is well documented throughout the Gospel accounts. Those that accepted Jesus also had a hard time letting go of their legalism. They proclaimed that they wanted those Gentiles to be circumcised (yikes) and to follow the law of Moses.
Paul and Barnabas stand up and proclaim that due to Jesus' sacrifice on the cross we were saved from the strictness and consequences of the law. Jesus fulfilled the law so that through his actions we could be saved. Before Jesus, strict adherence to the law was required for righteousness but this was no longer the case. Their main argument was: if Jesus had to die on the cross because we were unable to handle the burden of the Law then why should we place that burden now on the Gentiles? We are setting them up to fail that way.
The Council looked to Scripture for the answer and upon study James, the brother of Jesus, found the prophecy from Amos 9:11-12 that foretold the entry of the Gentiles. He said that they shouldn't make it difficult for the Gentiles to join since God wanted them to join. Scripture provided the answer they needed. This set the example for the other councils that came forth later on and from which we get the Apostle's Creed and the Nicene Creed.
They drafted their statement and sent a letter to the Gentiles informing them what they should do. They wanted them to keep from eating food sacrificed to idols, consuming blood or the meat of strangled animals, and from sexual immorality. The church found some unity in what needed to be avoided and what practices were no longer necessary.