The children of God will have a beautiful life—blameless and innocent (Romans 16:19 and 1 Thessalonians 3:13). Thus, they are children of God without blemish.
The characterization of the crooked and twisted generation is reminiscent of Deuteronomy 32:5. However, there is a difference. There Moses refers to the people of Israel. Here Paul typifies the pagan world of Philippi. The words denote a corrupt and deformed society. Christ has also used such characterizations in a different context (see Matthew 17:17 and Luke 9:41).
However degenerate and corrupt society may be, Christians do have an important vocation in their environment. They are called to shine as lights in the world. The world here refers to the world in general. This call insinuates that the world is dark, hostile to God. Compare Jesus’ call in Matthew 5:16, and what Paul writes in Ephesians 5:8 and 1 Thessalonians 5:5.
15 that you may be blameless and innocent, children of God without blemish in the midst of a crooked and twisted generation, among whom you shine as lights in the world,