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.