The disciples, and by extension, the elders of a local church are given the authority to bind and loose on earth. We see this reflected in Matthew 16:19 when Jesus is speaking to Peter after he made the confession that Jesus is “the Christ, the Son of the living God.” Likewise, in Matthew 18:18, Jesus extends the keys of the kingdom to the disciples. They can bind and loose on earth and so it will be in heaven.
So what are they (and by extension “we”) binding and loosing? People. The church is made up of people and when we read the context of Matthew 18:15-18, we see that Jesus makes this statement while speaking about church discipline. Essentially, the church is made up of people who confess Christ as the Son of the living God and at the same time are obedient to the teachings of the apostles (Scripture). When people deviate from this confession or are disobedient to the teachings, then the church leadership can decide to discipline them with the desire to restore them to right fellowship. Such discipline binds the flock, but also in situations where a person is unrepentant of their sin, the person is unbound.
Situation of conflict and sin
In Matthew 18:15-18, Jesus is providing His disciples guidance on how to handle a situation of conflict and sin in the congregation. First, the offended party should meet with the offender to be reconciled and for the offender to repent of his sin. Should there be a refusal to repent on the part of the offender, the situation is escalated to two or more faithful witnesses, following the Old Testament requirements where legal judgments were made on the testimony of two elders. Lastly, if there still is no repentance, the entire church is involved. When the person fails to come to his senses and does not repent of his offense, the church is charged to disassociate with that person; treat the offender as an unbeliever, removing their right to influence the church or to be counted among the flock. Such a disassociation does not warrant the church to neglect this person or wish them harm, but rather to be lovingly praying for and seeking after this person so that they may be right with God (see e.g. 1 Corinthians 5:5).
These actions of the church, and particularly the elders, are what Jesus calls “binding and loosing.” Where the church is gathered to judge on such matters of discipline, Jesus is with them and provides such authority to His faithful followers.
Reason to continuously pray
All this gives us reason to continuously pray. We are to pray for our church leaders that they would faithfully lead, shepherd and guard the flock. But, in addition, we are to pray that they would lovingly discipline those who may wrongly suppose that they are in good standing with God when their lives and confession are not in line with God’s will and God’s word. Finally, purity of the church is important, but the angels rejoice over a sinner who repents, and so shall we. As we pray for the church, let us pray that many people who are in the “visible” church and those outside would beautifully resign from their pride and sin, and turn to Jesus Christ.
Get a good introduction about the Bible in What is the Bible?