What does Matthew 5:16 mean?

Jesus has described His disciples as first the salt of the earth and then as the light of the world (Matthew 5:13–15). Salt is meant it be salty and becomes worthless if it loses that quality. Light is meant to be seen by those in the darkness. It has no value if covered up and hidden.

This verse provides the practical application of Jesus' teaching about being "the light of the world." Disciples display the light of Jesus by doing the good works which God intends for them. Even if acting in a Christlike way earns persecution from the world (Matthew 5:11–12), believers are meant to shine that light into a dark world. In other lessons, Jesus expands on the meaning of doing good works. An important point He makes later in the Sermon on the Mount involves proper motivation (Matthew 6:1). Good works done for God's sake, in ways that bring glory to God, ought to be done so that they can be seen. The light of Christian goodness is meant to shine out "so that" God will be glorified. However, in situations where the world is likely to merely praise the Christian, it's better for the act to be done "in secret" to avoid arrogance and pride (Matthew 6:2–4).

Christ is the only spiritual light in the world, and that truth is distributed through His people: His disciples, meaning born-again Christians. Believers do good for others to point towards truth (John 14:6), and to bring glory to God.