It acts as bleaching agent due to the release of nascent oxygen. Thus, the bleaching action of hydrogen peroxide is permanent and it is due to oxidation. It oxidizes the colouring matter to a colourless product.
${\mathrm{H}}_2{\mathrm{O}}_2\to {\mathrm{H}}_2\mathrm{O}+\left[\mathrm{O}\right]$