As Jesus established the order of the kingdom with his disciples he gave them insight into how conflicts within the community should be handled. Jesus described a process that works from deep humility, a process seldom followed well today.
The procedure he described paralleled that which was followed in the day, where unresolved disputes were brought before the Sanhedrin -- the Supreme Court -- for resolution. The Sanhedrin's decision was final, considered to be supported by God.
It seems in Matthew 18 Jesus is setting up his new Sanhedrin for settling conflict in the church. And, according to the foregoing conversation, they should make decisions in deep humility and holiness. Within these parameters God's authority is delegated and enabled.
Sanhedrin means people sitting together (gathering) and refers to the elders gathered to hear cases. Each town in Israel had a Sanhedrin of at least 23 men to try court cases and conduct business. They were usually the elders of the community, or heads of extended families. In Jerusalem was the Great Sanhedrin, composed mostly of priests and presided over the High Priest.