What does this equation mean?

Strip the history away and the mechanism is this: an environment — air, ambient light, the cosmic microwave background, phonons in a solid — continuously scatters off any system it is coupled to, and each scattering event carries away a small amount of information about that system’s state with respect to one particular observable, typically position. States that are eigenstates, or near-eigenstates, of that monitored observable are left almost undisturbed by the scattering; a photon that reflects off an object localized at x still tells you, afterward, that the object was at x , and nothing about the interaction has to change for that to remain true on the next scattering event. A superposition of two well-separated positions, by contrast, is not an eigenstate of position, and the environment cannot scatter off it without the scattered photon or molecule becoming entangled with which branch of the superposition it scattered from. Trace out the environment — which is the only thing an observer confined to the system can ever do — and the interference term between the two branches is gone, not suppressed slightly but multiplied by a factor that falls toward zero after a single scattering event and keeps falling with every event after that.