The first two clauses are formulas which occur often in letter writing, but the third is a characteristic addition made by the writer.
I pray: in the New Testament the Greek verb usually indicates prayer to God, but in letters of the time it was used in the nonreligious sense of “to wish,” “to hope.” In this passage it most likely has the latter meaning.
That all may go well with you, or ‘that you may be well in all respects (or in every way),’ ‘that good may always happen to you.’ The reference is to well-being in general. The Greek verb used has the literal meaning of “to be-led-along-a-good-road,” then, “to get along well,” “to succeed.”
That you may be in health, or ‘that you may be healthy,’ ‘that your body may be strong,’ ‘that you may be always new,’ ‘that you may not be sick (literally may be not-dying).’ The receptor language may prefer to mention the specific before the more generic. In such cases the present clause, which specifies an aspect of being well, has to be placed first.
I know that it is well with your soul, literally “as your soul is well.” The first clause, which uttered a wish, is now driven home by a reference to a fact. Therefore several versions have added ‘I know,’ or ‘surely.’
The verb “to be well” is the same as that in the first clause, but now the reference is not to the bodily and material aspect of man. To make this clear the writer has added with your soul, in which soul refers to the spiritual aspect of the human personality. Compare such renderings of the clause as “you are well in spirit” (Good News Translation), ‘your innermost remains as good as that,’ ‘as you are well in your head-heart.’
Quoted with permission from Haas, C., de Jonge, M. and Swellengrebel, J.L. A Handbook on The Third Letter of John. (UBS Handbook Series). New York: UBS, 1972. For this and other handbooks for translators see here .