Photons have no mass, but they do have energy, which is proportional to their frequency. We are familiar with this type of energy at various frequencies — microwave ovens are one example, visible light is another. The fact that light has energy is obvious (you can feel the heat).
In the case of solar sails, much of the energy doesn’t turn into heat. The sail is reflective, so it absorbs little energy, and, therefore, the light particles bounce off the sail. As they do, they transfer momentum from the light to the sail, producing a force. This reflective sail gets a double kick: one push from the sail stopping the photon and one from reflecting the photon and accelerating it away. — LOUIS FRIEDMAN, EXECUTIVE DIRECTOR, THE PLANETARY SOCIETY, PASADENA, CALIFORNIA