Jesus tells his disciples that he is like a vine and God is the caretaker of the vineyard. He's never out of metaphors, this one.
God cuts off all the branches on the vine that don't grow grapes. The branches that do produce grapes, though, he prunes and trims, so that they can make even more beautiful, delicious grapes. Everyone wants to be a delicious grape.
Without Jesus, the branches can't grow at all. If people don't believe in him, their branches will be cut off from the vine and end up dead and withered. Branches like that are usually gathered up and thrown in a bonfire. Very subtle, Jesus.