Individual atoms or ions can be excited to "meta-stable" states, from which they can decay via emission of forbidden light, by other photons (usually X-ray or UV) or by energetic collisions with other particles.

It has nothing to do with black holes, except that accretion disks around black holes can, due to their high temperature, produce the necessary energetic photons. (But so can massive stars, for example.) The rotational energy of the black hole is not involved.