What does Matthew 5:13 mean?
Matthew is recording Jesus' Sermon on the Mount. The prior passage recorded the Beatitudes, and now Christ turns to a series of short teachings on various topics. First, He addresses the need for disciples of Jesus to live according to the virtues described in the Beatitudes. These are needed in order to be "salt" and "light" in the world (Matthew 5:14).Jesus says to His disciples, "You are the salt of the earth." Then, as now, salt served a variety of functions. Before the days of refrigeration, salt was used widely as a preservative by rubbing it into meat. In some cases, it could be used as a kind of fertilizer. Also, of course, it was used to bring flavor to food. Jesus' call for followers to be "salt of the earth" carries those uses, symbolically, into our spiritual lives.
As salt preserves meat from rotting, believers in Jesus, distributed around the world, help to preserve humanity from falling into godlessness, immorality, chaos, and the resulting judgment. Salt permanently changes the flavor of food, just as the influence of godly people can change a culture. The main point is that Christians serve a godly purpose in the world simply by living out what we believe about Jesus.
Christians stop serving that purpose when we stop living in faithfulness to God. The recent references to the Beatitudes put that purpose in context. When Jesus' followers stop being poor in spirit, living in repentance and meekness, having an appetite for righteousness, and being merciful, they stop serving their purpose on earth. This is just as catastrophic, and unthinkable, as if salt were to lose its flavor.
Some object to this metaphor by saying that salt never loses its saltiness, according to chemistry. This misses the point and is not true in a practical sense. Jesus' teaching can be taken to mean, in part, that certain qualities are as innate to a born-again believer as saltiness is to salt. The idea of losing those properties is unthinkable. In a more practical sense, the salt which people used daily was not chemically pure. It could be diluted, or even contaminated. That would result in something that was supposed to be salt but didn't taste or act like salt anymore. That made it useless, and subject to disposal.
Jesus indicates the same can happen to a disciple who stops living faithfully to Christ in the world. The point here is not about loss of salvation, but a loss of purpose. "Bad salt" isn't destroyed or burnt, it's simply ignored along with the dust of the earth.