When the word branch is used in scripture, it should remind one of Christ’s description of Himself in John 9:10. Christ compared Himself to a “true vine” to which all must connect if they are going to bear fruit. Christ inspired prophecies about a coming servant. All should be His servants. For any of His servants to produce “fruit” they must connect with Him, “the true vine.” Life comes from that connection. All are preserved by Christ, nourished by His word, and the sacrament prayers ask that we always have His spirit to be with us. The “vine” and “fruit” refer to the “family of God.” The context is about becoming a “son of God.”1
1 Preserving the Restoration, 34–35.