John tells Gaius that he is doing well in being faithful towards strangers working for God’s glory. He mentions that Diotrephes does not accept their authority and also refuses to welcome fellow Christians. John tells Gaius to keep to what is good, as it is from God. Those who do not do good have not seen God.
Who wrote it?
3 John is identified as being written by someone named John, and there is support for the view that this was indeed the apostle John who wrote the Gospel of John.
Who was it written to?
3 John 1:1 addresses the letter to Gaius, a fellow Christian who John was close with.
When was it written?
1 John, 2 John, and 3 John were most likely written towards the end of the 1st century A.D. 1 John is mentioned in a few early church writings from the early 2nd century. Near the end of his life, John was reportedly ministering near Ephesus, perhaps when he wrote these letters.
Why was it written?
3 John was written to encourage Gaius and to tell him to walk in goodness even though he may encounter opposition.
How does 3 John apply to me?
3 John is a short letter that illustrates the goodness of hospitality and imitating good (God). As Christians, we are to receive our fellow Christians warmly, even those who are strangers. We are not to become like those around us if they do not imitate God.
As for all posts in this series, a book introduction in a good study Bible will provide more information than listed here. The ESV Study Bible is one recommendation.
The Bible Project video on 3 John (covers 1, 2, and 3 John)