In classical physics, it is always possible to theoretically separate a particle from its environment. For example, in the Earth – Sun system, we can define our system to being Earth + Sun and study its interactions to determine the motion of the Earth, or, alternatively, we can define our system as being just the Earth; in this case, the effect of the Sun enters through an external gravitational potential field.
However, this freedom to choose the system as either Earth – Sun or just the Earth is not possible in quantum mechanics. The reason is that in quantum mechanics of many particles, there is a phenomenon, called quantum entanglement, which has no classical counterpart. Two quantum particles are said to be entagled if it is impossible to describe one of them without describing the other. The two particles become a single system in a way that no two classical particles ever would. It is now not possible to choose as the system only one of the particles and include the effect of the other one as an external potential field. This phenomenon has been well known since the early days of quantum theory, and has led to several paradoxes like the famous EPR paradox.
An apparently unrelated problem is why we perceived the macroscopic reality as classical when the microscopic reality is quantum in nature. An early explanation of this was the Copenhagen interpretation of quantum mechanics. It says that quantum systems are in a superposition of states, and a measurement causes their wave function to collapse into one of their eigenstates, giving a well defined value of the quantity measured. However, this requires that reality as we perceive it is created by the action of the measurement, which led to paradoxes like the famous Schrödinger's cat.
A better interpretation appeared in the 1980s. The key idea is that of quantum entanglement between a particle and the particles that constitutes its environment. Consider for example a macroscopic particle freely moving in space, but being constantly hit by photons. The photons transfer very little momentum to the particle, so, classically, we can ignore the photon scattering when we are dealing with the motion of the particle. However, in quantum theory, each of these photons that het the particle will become entagled with it, and now we have a quantum system containing the particle and millions and millions of photons. Since the particle is entagled with the photons, we cannot use quantum mechanics to describe the particle alone; we need to consider the particle plus all the photons. And here is the point: it can be shown mathematically that when millions of particles become entagled, the typical quantum mechanical phenomena get “diluted” in the whole system, and the particle can now be described classically. This is why microscopic systems exhibit quantum behaviour and macroscopic systems don’t: Atoms can get entagled with particles in its environment, but not with enough particles to make quantum effects disappear. Macroscopic objects, due to their side, get entagled to millions of particles, and quantum effects just fade away.
Now, coherence is a measure of how much the system can be described by quantum mechanics (This is an informal definition, coherence is actually precisely defined, but that goes beyond the scope of this article). Then, this dispersion of quantum effects when we go to the macroscopic world is what is called quantum decoherence.
This theory has been well confirmed by experiments. For example, an experiment with molecular diffraction was carried out in which air was slowly introduced in the tube where the molecules were accelerated. The diffraction patterns produced by the molecules started to fade away the more air enters the tube. Since molecules diffraction is due to the wave nature of molecules, which is a quantum phenomenon, the introducing of air in the tubes mean that the molecules will interact with more particles, therefore will become entagled with more particles and their quantum effects will disappear, just as was observed.
What is remarkable about this is that the emergence of classical physics from quantum mechanics is due to entanglement, which is a strictly quantum mechanical phenomenon.