What is a photon and does it have mass?

They are the quanta of any electromagnetic field (wave) that can be detected whenever that wave hits something that is able to absorb its particular frequency of energy. In other words, whenever light strikes anything that has a natural resonance equal to its frequency, its energy (hF) is absorbed and that event is described as a photon. It has no rest mass but does have an amount of energy equal to its frequency (F) times Planck’s constant (h). It is affected by gravity because energy is the equivalent of mass (E=mc^2+hF). The mc^2 term is zero but the hF term is not and so acts as an effective mass.