The massive body (or group of bodies) acts like a lens, with an "index of refraction" that reflects the effect of spacetime curvature on the light path.
In English: Yes, it's space itself which is distorted; thus the light path is bent. As for the bending process, which is "refraction", try this. Place a pencil in a glass of water. The water's surface seems to split the pencil into adjacent halves.