I. John receives a good report of Gaius's faith and charity from the brethren. Gaius’s love for the brethren and hospitality to strangers proves his sincerity in the faith. II. Gaius is commended for his hospitality, a virtue extended to strangers and those of different churches. III. John expresses great joy in hearing of Gaius's walk in truth. This reflects the joy of ministers when they see their followers living out their faith. IV. John advises Gaius to continue supporting the brethren by aiding them on their journeys in a godly manner, reflecting Christian generosity. V. The brethren went forth preaching for God's sake, taking nothing from the Gentiles. John emphasizes the need for the church to support such ministers, as they help propagate the truth.

To hear that my children - From this it has been inferred that Caius was one of St. John's converts, and consequently not the Corinthian Caius, who was converted, most probably, by St. Paul. But the apostle might use the term children here as implying those who were immediately under his pastoral care, and, being an old man, he had a right to use such terms in addressing his juniors both in age and grace; and there is much both of propriety and dignity in the appellation coming from such a person.

I have no greater joy,.... Nothing that causes greater joy. The Vulgate Latin version reads "grace" or "thanks"; and then the sense is, that he had nothing to be more thankful for:

than to hear that my children walk in truth; meaning his spiritual children, those whose conversion he had been the instrument of; and among these it seems Gaius was one.

my children--members of the Church: confirming the view that the "elect lady" is a Church.