Ezekiel uses the illustration of a dead branch or vine to represent the people who claim to be following God, but are not truly doing so. A similar illustration, but with different emphasis, was used by Jesus in John 15 regarding the vinedresser, the true vine, and the branches. As children of God, the expectation is that we produce fruit. Otherwise, we are like branches that are useless. There's much in this chapter to ponder.
