The Greek word koinōnia is translated four times as “fellowship” in 1 John 1. John wrote the letter of 1 John to his readers to clarify what true Christian belief and living really were, primarily to assure them of the eternal life that they possessed (1 John 5:13). Assuming they held fast to what he wrote and thus possessed this eternal life, the readers would continue, as John said to his readers, to “have fellowship with us; and indeed our fellowship is with the Father and with his Son Jesus Christ” (1 John 1:3). John clarified that there is no “fellowship with him while we walk in darkness,” that is, there is no fellowship for those who persistently and unrepentantly live in sin while claiming to have eternal life (1 John 1:5). Rather, “if we walk in the light, as he is in the light, we have fellowship with one another” (1 John 1:7).
The word koinōnia in the NT simply involves sharing something or having something in common with someone else. For example, in 2 Corithians 8:4, Paul spoke of the koinōnia he enjoyed with the Macedonian churches, sharing the task of giving to believers in a time of famine. Similarly, a related word in Luke 5:10 (koinōnos) is translated “partners,” used to show that Peter, Andrew, James, and John shared a fishing enterprise together. The word koinōnia indicates something shared, and the context of a given passage will specify who is doing the sharing and what is being shared.
Though John does not explicitly state in 1 John 1:1–7 what is shared between himself, his readers, and the Father and Son, he at least indicates that he shared something (have fellowship) with them by having proclaimed to them the message of eternal life (1:1–3), something that they also shared with the Father and Son.
John proclaimed his eyewitness account of “the word of life” in 1 John 1:1. He then proclaimed that “the life…the eternal life” was physically revealed and now being proclaimed in his letter (1 John 1:2). It is clear that John’s proclamation is about eternal life. And, this proclamation is given in terms that physically describe Jesus as well (something seen, heard, touched, etc.). The message of eternal life is thus the message of Jesus who is Life Himself.
What is assumed is that his readers believed and thereby shared (or had in common) the message and person of Jesus in some way. If Jesus is eternal life, John and his readers had in common (or shared) possessing the eternal life that is found in the Father and the Son. It could be said that the Father and Son also shared (or had in common) this life with John and his fellow believers in that the Father and Son inherently possessed this life in and of Themselves.
For a far better and more thorough treatment of fellowship in 1 John that what you see above, click here to read “The Meaning of Fellowship in 1 John” by William W. Combs in the Detroit Baptist Seminary Journal.