This phrase is used to describe the blackout imposed by the Nazi regime in Copenhagen. While the blackout is meant to obscure the city from enemy bombers, it also creates a sense of overwhelming darkness. The phrase "bright darkness" highlights the paradoxical nature of this situation: a darkness that is somehow both oppressive and illuminating.
This oxymoron serves to emphasize the unsettling and paradoxical nature of the war and the Nazi occupation, where fear and danger co-exist with moments of courage and hope.