A screen scene is a scene in which an actor hides behind a drape or furniture and overhears the other actors. Melodrama, with its emphasis on secrets and their revelation, often makes use of the screen scene to allow a character to discover a secret. This discovery is a turning point in the plot.
In Lady Windermere's Fan, Lady Windermere's eavesdropping convinces her of her husband's fidelity. Also Mrs. Erlynne's sacrifice of her own reputation convinces her of the older woman's virtue.
Part of the purpose of the screen scene is to allow a character to discover information he or she is not supposed to hear. At the same time, the risk of being discovered in the act of eavesdropping adds to the dramatic intensity of the scene.