1. “I am the bread of life.” (John 6:35)
2. “I am the light of the world.” (John 8:12)
3. “I am the gate.” (John 10:9)
4. “I am the good shepherd.” (John 10:11)
5. “I am the resurrection and the life.” (John 11:25)
6. “I am the way, the truth, and the life.” (John 14:7)
7. “I am the true vine.” (John 15:1)

The nation of Israel.

“¹ Let me sing for my beloved my love song concerning his vineyard: My beloved had a vineyard on a very fertile hill. ² He dug it and cleared it of stones, and planted it with choice vines; he built a watchtower in the midst of it, and hewed out a wine vat in it; and he looked for it to yield grapes, but it yielded wild grapes.”
–Isaiah 5:1-2 (ESV)

“⁸ You brought a vine out of Egypt; you drove out the nations and planted it. ⁹ You cleared the ground for it; it took deep root and filled the land. ¹⁰ The mountains were covered with its shade, the mighty cedars with its branches.”
–Psalm 80:8-10 (ESV)

Jesus.

Israel as the vine produced sour grapes, and they were a degenerate and strange vine. However, Christ the true vine is perfect, and he produces much fruit. For believers, we find our identity in Christ and nothing else. Jesus is the vine that nourishes and energizes us. 

God the Father.

1. He cuts or takes away the branches that are not bearing fruit. Those branches represent those who profess to be Christians but are not producing fruit.
2. He prunes the branches that are bearing fruit. Pruning involves pain—it involves the Father shaping and molding us into the image of His Son.

The branches represent those who profess to be Christians and those who are genuinely saved. The false Christians will be cut off but the genuine Christians are encouraged to abide.

It means to remain, to find our identity in Jesus. Like the branches remaining in the vine so that they may find nourishment and life, believers are to remain in Christ.