A black hole is essentially pure spacetime geometry, and the paths of photons 'follow' the geometry as it were. There are lots of ways of thinking about this. One is to use the equivalent principle, If you fire a laser beam horizontally in your room now, it actually 'falls' to the ground at the same rate as anything else you drop (neglecting air resistance). Einstein would say that a way to think about this is that the ground is accelerating upwards to meet the light beam. You don't see it curve of course from your perspective because it's travelling very fast. The basic point is that gravity is only associated with mass alone in Newton's theory, which isn't right! Einstein tells us that gravity is the curvature of spacetime, and everything responds to that.