Jesus often used scenes from the countryside for his parables. The vine would be a familiar sight in Palestine. When Moses was in the desert he sent spies to the land of Canaan to see what it was like and they brought a bunch of grapes as a symbol of the richness of the land (Numbers 13:23).
Jesus came to join himself to humanity, as vine to branches. Without him the branches are lifeless. His body and blood are like the sap flowing through the vine. He gives the image of the Father as the vine dresser. Vines have to be severely pruned in order to make them fruitful. In a lifetime there are many choices to be made and roads to be taken. Often it is necessary to let one thing go so that there is space for something else. The pruning can take many forms: a disappointment, a humiliation, a gentle nudge towards something, a loss or some painful remark which results in fresh thinking.
This passage forms part of what are called the Last Supper discourses. John has made them part of the event as a body of key teaching that Jesus would want his friends to remember as he took leave of them. In particular there are the beautiful revelations of the persons of the Trinity.