A photon sphere is a sphere-shaped surface (or, in some cases, oblate-spheroid-shaped) around a black hole at just the distance so photons can orbit the black hole, i.e., any orbiting photon will be located on it. For a non-rotating black hole, it is 3/2 the Schwarzschild radius from the center of the black hole. Within the photon sphere, no object can maintain an orbit without accelerating (e.g., assisted by a constant force): it will either fall into the event horizon or escape the black hole. This phenomena is entirely due to the strong-field gravity, and in theory, a neutron star could be dense enough to have an external photon sphere: I assume if it were non-rotating, it would be at 3/2 its calculated Schwarzschild radius. For a rotating black hole, there are two nested photon spheres, one within the ergosphere and another external to it.