This phrase that Jesus uses "I am" is the last self-designation that He makes in this gospel, and describes the relationship between Him and his disciples, his background is Isaiah 5.1-7, where Israel is compared to a vineyard lovingly cared for by God , but unlike Israel, Jesus is the true vine; that is, real, genuine.
The branch that does not bear fruit is destroyed, the immediate reference was probably to Judas, but the idea applies to all the pseudo-believers.
The fruit that the farmer desires for his people is the similarity with Christ. For a branch to be productive it has to be pruned; that is, subject to the beneficent discipline of the Father, and must be kept tightly bound to the vine. When we remain in Christ, our prayers are effective, we glorify God by bearing fruit, we show our condition as disciples, and we experience the fullness of joy as we receive in our hearts the joy of Christ.