What does Romans 14:19 mean?

This sums up what Paul has written in the previous verses. He is urging those who are strong in faith to be willing to set aside the open exercise of their freedom in Christ, if necessary, to keep from harming the faith and obedience of those who are less strong. For example, believers should be willing to forego eating meat if that will keep those "weak in faith" (Romans 14:1–2) from stumbling into violating their own conscience.

This willingness to defer our own rights, to set aside our freedom in Christ for the sake of others, is itself a service to Christ. It results in peace and encouragement for everyone. Paul urges these strong Christians to pursue that peace and mutual encouragement by setting themselves aside for the good of their brothers and sisters.

As with other verses in this chapter, Paul's point here is not to give more legalism-minded believers the right to police the actions of all other Christians (Colossians 2:16–23). Christians do not lose their liberty because of the opinions of others (Romans 14:3; 1 Corinthians 10:29–30). Rather, they ought to discern the difference between exercising freedom and abusing it.