Resignation determines how resigned to their fate captives are overall. It is controlled by various factors, such as the amount of fear, order, and awe they are subjected to, as well as their levels of feasting, resting, and religion.
Keeping captives resigned is important since, if their resignation levels get too low, captives with high courage may attempt to escape the island, potentially alerting foreign nations to your location and leading to an invasion. Captives with both high courage and high leadership may even lead a captive revolt. Of course, you can have captives released, ransomed (wealthy and skilled captives only), press ganged (unskilled captives only), or assassinated (worker captives only).