What is a photon sphere and how is it created?

Black holes are so gravitationally powerful, nothing can escape their pull, not even light (photons). However, photons with enough energy traveling in the vicinity of a black hole are bent in their direction by the gravitational pull of the black hole. Those with not enough energy start orbiting the black hole in a sphere, called the photon sphere. 

Black holes are invisible to the naked eye, as all we could see is the accretion disc and the photon sphere, located near the event horizon. 
These photon spheres are highly unstable and pretty short lived, as photons tend to get swallowed by the black hole. If someone could stand inside a photon sphere, the velocity of the spin of the photons orbiting the black hole would make it possible to see the back of your own head. 
In case of a rotating black hole, there are two different photon spheres: the one closer to the event horizon spins the same direction as the black hole. The second photon sphere, further away from the event horizon spins in the opposite direction. – Roman Alexander

(The question was originally asked by Bhuwanesh Singh from India)