Jesus repeats Himself for emphasis. What He is saying is very important and He does not want His disciples (or us) to miss the point. This is also the last of His “I am” statements.

Jesus (through John) uses the emphatic pronouns for “I” and “you” and sets them against each other to make sure that the roles of Christ and His followers will not be confused. His illustration of the branch and the vine give us a very pretty picture of what and how we are to abide in Him. (The following is adapted from “Abide in Christ” by Andrew Murray)

1. We are able to see the nature of that union. The connection, or relationship between the vine and the branch is a living one. It is permanent and is not the work of the branch, but of the vine. Our union with our Lord is the work of God, and not of ourselves. He has made the relationship between us and His Son to be so close and complete that the same Spirit Who dwells in Jesus now dwells in us (Gal 4:6). Just as between the branch and the vine, this is a life union between us and Christ that makes us one.
2. We are also able to see the completeness of that union. The relationship between the branch and the vine is such that each is nothing without the other.
   1. Without the vine, the branch can do nothing. In our verse, Jesus tells us that “apart from me you can do nothing.” We can only be pleasing to the Father when we do everything through the power of Christ, Who lives in us by His Spirit. We must be utterly dependent upon Him.
   2. Without the branch the vine can do nothing. This is the more difficult of the two for us to accept, and yet so true! Without the branch, the vine produces no fruit. Grapes are only produced by the branches. What an incredible thing that as totally dependent upon Him that we must be, so has He made Himself to be that dependent upon us! Without His disciples on this planet, He cannot bring salvation to those who are lost. It is only through us that His fruit may be found. This aspect of the process is not an afterthought on His part, or something which He was backed into a corner about; He wanted it this way. He deliberately chose to make his redeemed ones to be an indispensable part in the salvation process. What a high honor and yet what a great responsibility that without us He can do nothing!
      “As neither vine nor branch is anything without the other, so is neither anything except for the other.” (Murray)
   3. All the vine possesses belongs to the branches. The vine does not live for itself; it gains the nutrients and water from the soil so that it can supply the branches. Everything it has is at the disposal of the branches. In the same way, all the fullness of Christ, all of His riches are ours. “All that Jesus is in heaven, He is for us: He has no interest there seperate from ours; as our representative He stands before the Father.” (Murray)
   4. And all the branch possesses belongs to the vine. The branch does not live for itself, but to produce fruit which brings glory to the vine. The branch has no other reason for existence. Everything that we have and everything that we are belongs to our Lord.
3. This illustration also teaches us the object of the union between the branches and the vine. The branches exist to produce fruit and fruit alone. They have no other reason for existence. The branch needs leaves to gather the sunshine and maintain its own life and produce the best possible fruit, but the fruit itself, the branch gives away. The branch gives away the fruit which it produces to others, and not to the vine, but the result is that the vine is glorified. Whoever takes the fruit and notes its quality praises the vine for it. So it is with us. It is for fruit, and for much fruit that the Father has brought us into union with His Son.

“On my part, abiding is nothing but the acceptance of my position, the consent to be kept there, the surrender of faith to the strong Vine still to hold the feeble branch.” (Murray) Apart from Christ we can do nothing, but the converse is also true (Php 4:13).

Philippians 4:13  I can do everything through him who gives me strength.