The letter we know as 3 John is the only true private letter we have in the New Testament. Kruse (218; quoted in the sub-points) points out three functions 3 John exemplifies:
(i) to reinforce Gaius’s commitment to the noble work of providing hospitality to travelling missionaries, something he was already doing (vv. 5–8)
(ii) to draw attention to the intolerable behaviour of Diotrephes and to foreshadow the steps he intends to take in response to it (vv. 9–10)
(iii) to commend Demetrius (v. 12)
In the opening greetings we read: “The elder to Gaius the beloved, whom I love in truth [or: truly; the phrase “in truth” (ἐν ἀληθείᾳ) can be either rendered “in the truth” (sphere) or “truly” (adverbial)]” (v.1; AT).
We know little about the person of Gaius and his name was common in the Roman Empire. The footnote in the NET reads that “, it is highly unlikely that the person named here is to be identified with any of the others of the same name associated with Paul (1 Cor 1:14, Rom 16:23 [these two references are probably to the same person]; Acts 19:29, Acts 20:4).” All the information we have is to be found in 3 John. We know from this letter that Gaius is well known to the author of 3 John (maybe only via written/oral correspondence) and that he is a faithful and orthodox minister of God and in that sense a co-worker against the secessionists. Further, that the elder uses the personal pronoun “I” (ἐγώ) might intensify the expression of his love to Gaius.
Verse 2: “Beloved, I pray that all may succeed [go well] with you and you be healthy, as it is well with your soul” (AT). Stowers (Letter Writing in Greco-Roman Antiquity, 73) “notes that the wishes for well-being or prayer (like that found in v. 2) occur in about one third of the papyrus family letters (as distinct from friendship letters)” (Kruse, 221 n. 3). This part of the letter where on establishes rapport with the audience is called exordium. Again Gaius is called “beloved” (ἀγαπητέ, see also vv. 5, 11) as in verse 1. In Greek the word ψυχή “is used in the Johannine writings to mean simply one’s natural life (so, e.g., John 10:11, 15, 17; 12:25; 13:37, 38; 15:13; 1 John 3:16)” but its other connotations is a reference to “one’s inner life as distinct from one’s body (John 10:24, 27)” (Kruse, 221). John is wishing that all does go well with Gaius as his soul is well already.
John continues to state (v. 3; AT): “For I rejoiced exceedingly when the brothers came and testified to your truth, as you walk in the truth.” Here we can see now why the author could assert that Gaius’ soul is well. It is well because others have testified to “your truth” (σου τῇ ἀληθείᾳ). This phrase indicates the truth to which Gaius is adhering and probably his teaching as well (σου is a subjective genitive). Not only is orthodoxy present but orthopraxy as well; this is indicated by “As you walk in the truth” (καθὼς σὺ ἐν ἀληθείᾳ περιπατεῖς). This is tremendously crucial for us today; right conduct flows out of a right understanding and theology.
This orthopraxy is seen to be in terms of hospitality in the later verses. It is of interest to observe that “[i]n all three letters of John the author’s joy is said to be complete when the readers maintain fellowship with him and walk in the truth (1 John 1:4; 2 John 4; 3 John 3–4)” (Kruse, 221).
The elder further writes (v. 4; AT): “I do not have greater joy than this that I hear that my children walk in the truth.” And then says: “Beloved, you do a faithful thing (by) whatever you do towards the brothers (even though they are) strangers” (v. 5; AT). Raymond E. Brown, The Epistles of John (AB 30, New York: Doubleday, 1982) 740–41 suggests that the hospitality shown by Gaius might be due to the evil behavior and refusal to invite the guests by Diotrephes. Gaius had been the “guarantor of their bona fides to the rest of the community” (Kruse, 223). The aspect of hospitality again implied more than to provide a place to sleep and food to eat (as seen in 2 John already; see there for comments).
These brothers (though being strangers) have testified to Gaius love (v. 6; AT: “who testified to your love before the church, whom you do well to send on their way [in a manner] worthy of God”). Here the word to “send” is a form of προπέμπω which is defined by a lexicon thus: “to send someone on in the direction in which he has already been moving, with the probable implication of providing help—‘to send on one’s way, to help on one’s way’” (LN 15.72). The term προπέμπω “functioned as a technical term for missionary support in the early church (cf. Acts 15:3; 20:38; 21:5; Rom 15:24; 1 Cor 16:6, 11; 2 Cor 1:16; Tit 3:13)” (Kruse, 223). We also note that at this point we have the first occurrence of “church” (ἐκκλησία) in Johannine literature (see also verse 9 and 10 as well as many references in Rev).
These brothers “went out for the name’s sake, receiving nothing from the Gentiles” (v. 7; AT). Normally in the Johannine letters the term “went out” (ἐξέρχομαι) is in reference to the secessionist, but here it is toward the true missionaries of Christ. Because they went out for the name’s sake “we ought to assist such people, so that we may become coworkers for the truth’s sake” (v. 8; AT). The third reason why it is “worthy of God” to send these missionaries out is given here. This is so, because in so doing we participate in the gospel work (the first two reason were  they went out “for the name’s sake” and  they got no help from anybody else; see v. 7).
Coming from faithful Gaius and these truthful Christian missionaries, John turns to a man called Diotrephes who is in opposition to the elder. Verse 9 (AT) reads: “I wrote something to the church, but Diotrephes, who wishes to be better than others, does not obey [or: acknowledge] us.” That Diotrephes liked to be “better than others” (φιλοπρωτεύων αὐτῶν) might imply the grabbing for leadership and power. “To reject the ‘brothers’ recommended by the elder was the same as rejecting the elder himself. This way of thinking is common in the Fourth Gospel, where to receive the ones sent is the same as receiving the one who sent them (cf. John 5:23; 12:44–45; 13:20; 14:24)” (Kruse, 227).
Now the elder goes into more details about his plans. “Therefore, if I come, I will remind (him) about the works he does, talking nonsense with evil words against us; and not being content with this, neither does he receive the brothers, and those who wish to do so he hinders and throws them out of the church” (v. 10; AT). Kruse again comments that there a four aspects to Diotrephes’ misconduct (the following is quoted from Kruse, 227):
(i) malicious gossip about the elder and his community
(ii) refusal to welcome the orthodox missionaries
(iii) preventing others from doing so
(iv) putting out of the church those who defied him in this matter
“Such action, a form of public rebuke, would be required of the elder in the culture of the first-century Mediterranean world to restore the honour he had lost when Diotrephes spoke evil of him” (Kruse, 227). What else could the elder do to restore gospel ministry? The gospel needs to proceed and no one (even those inside the church!) can hinder its progress.
“Beloved, do not imitate such evil, but the good. The one who does good is from God; the one who does evil has not seen God” (v. 11; AT). The “good” might refer to provide hospitality, whereas the “evil” is the refusal of such. He who welcomes Christian missionaries and workers does good and participates in that way in gospel ministry.
A new character is introduced. He is another faithful servant of Christ. “To Demetrius it has been testified by all and even by truth herself. And we also testify, and you know, that our testimony is true” (v. 12; AT).
The final greetings given by the apostle are: “I have to write many things to you, but I do not wish to write to you with ink and pen” (v.13; AT; see comment on 2 John 12). “I hope to see you immediately, and we will talk mouth to mouth [i.e., face to face]” (v. 14; AT). Kruse states that “[t]he expression of a desire to communicate face to face rather than by letter is typical of the friendly letter tradition of the first-century Mediterranean world” (233-34). This again shows the friendship between Gaius and John.
“Peace to you. The friends greet you. Greet the friends by name” (v. 15; AT). That John writes “friends” instead of “brothers” comes as a surprise. This is the only occurrence in the New Testament were believers are addressed as friends. But Kruse seems to be right when he states: “It may have derived from Jesus’ description of his disciples as his ‘friends’ in John 15:13–15” (234).
This post was just a quick exposition of 3 John. In conclusion I would like to point out two implications for us today. One is that orthodoxy (right belief/doctrine) and orthopraxy (right behavior/conduct) need to go hand in hand. One of those should not be neglected and neither should be exalted above the other. I am strongly convinced that theology does influence (“determine”) our behavior.
The other implication I would like to point out is the necessity to partake in kingdom work. This looks different for each one of us—some are sent, some are there to support—but we all participate with one another. Even though if you are not sent (in the sense of being called to “foreign mission”), you are sent into your workplace, school, office etc. to be a witness of Jesus and his amazing love!