The KJV translation mildly obscures the picture that would have been the model for these phrases. In the cultural climate of Israel there were frequent litigations. Thus the adversary is a legal adversary, not necessarily an enemy. The scene takes place as both are “in the way” to the judge. Thus the example is two people with a disagreement who are on their way to the judge for adjudication.
The unfortunate conclusion to this experience was typically the imprisonment of one person for debt, and the debt was to be paid prior to the release of the person from prison. The 3 Nephi redaction attempts to move the basic scene out of the Old World context, but the nature of the language of the KJV obscured the basis for the incident, so the transition is incomplete. Joseph excised the references to the judges and officers, but retained the language of the adversary and the jail.
In the Mesomaerican context there is not indication that there was anything known as debtor’s prison. Later Mesoamerican societies resolved indebtedness through slavery, not debtor’s prison. The additional text on verse 26 refers to the difficulty of paying debts while in prison and away from resources. That would be very understandable to Joseph and his cultural milieu, but foreign to both the Mesoamerican and ancient Old World settings. In such cases, the extended family is responsible for the debt, and those people are still in contact with their resources.
The nature of the changes in this verse revolves around a more modern cultural assumption, combined with the attempt to rewrite the Matthean text into the Book of Mormon context (such as replacing farthing with senine).
As a continuation of the explanation of how anger is to be avoided, it is an expansion of the people approaching the temple (or the Savior). They are to “fix” their anger prior to approaching the sacred. In the secular world, they may be approaching a judge, and they should settle their differences between themselves before submitting to a judge (who many not know them). Thus this is the same basic instruction as the previous verses, except that the context is secular instead of religious.