Bleaching properties of bleaching powder are due it its:
Chlorine bleaches by the process of oxidation. It needs moisture for its bleaching action.
Chlorine reacts with water to form hydrochloric and hypochlorous acids.
Cl2+H2O→HCl+HClO
Hypochlorous acid is unstable, and it easily dissociates to form nascent oxygen.
HClO→HCl+[O]
Nascent oxygen is a more powerful oxidising agent. Its formation is responsible for the bleaching nature of chlorine in the presence of moisture.
Hence option A is correct answer.