In simple terms, radiation pressure is simply pressure exerted on any surface exposed to electromagnetic radiation. According to the Maxwell formulation of electromagnetism, an electromagnetic wave carries momentum. This momentum can be transferred to any surface hit by the wave. Radiation pressure can also be understood in the context of special relativity, where photons are defined to have energy E = pc. Since momentum is always conserved, photons striking an absorbing surface must transfer their momentum to that surface.
It can be shown using basic thermodynamics that the pressure exerted on a surface due to isotropic radiation is
where T is the temperature of the thermal radiation, σ is the Stefan-Boltzmann constant, and c is the speed of light.