The First Reading tells how, three years after his conversion, Paul went up to Jerusalem. In spite of being introduced by Barnabas, such was the hostility he encountered that he had to be smuggled out of the city. The fact that Paul took all these trials in his stride shows the depth of his faith in Jesus.
The Second Reading tells us what we have to do in order to be at rights with God. We have to believe in his Son, Jesus, and love one another as he told us. Active charity is what distinguishes true Christians from those who are such in name only. (This is what makes them fruitful branches of Christ, the true vine.)
In the Gospel we have the lovely image of the vine and the branches. Here Jesus stresses the unity that exists between him and his disciples. Vine and branches need each other. The vine cannot bear fruit without the branches. And the branches can have no life if separated from the vine. The branches need to be pruned (by trials) in order to be fruitful. St Paul is a good example.