Taking disagreements to a judge
During that time, people who had disagreements pleaded their case before a judge, and the judge alone determined how the disagreement should be settled.
In the United States today, the court system is divided between criminal cases where the government takes a person in front of a court to try him for a crime, and civil litigation, where a plaintiff takes a defendant to court over a conflict and seeks a particular judgment from the judge.
Jesus’ statement here could well be applied to civil cases, where the plaintiff and defendant could easily reach a settlement prior to the trial to avoid wasting judges’ time and taxpayers’ money. Again, it must be noted here that many of Jesus’ teachings are meant for a particular time and circumstance. As such we are cautioned to try to over-extend their meaning beyond their practical purpose.
The biggest takeaway point here is to “settle matters quickly with your adversary” before they become bigger issues. This relieves us of the focus and attention on petty matters, allowing us to utilize more of our time to grow spiritually. The most important focus in our life should upon reviving our relationship with God.
This is why Jesus' most important teaching was:
“‘Love the Lord your God with all your heart and with all your soul and with all your mind.' This is the first and greatest commandment." (Matt. 22:37-38)