I only yesterday saw this question, I am sorry.
The answer is simple. Consider a quantum system described by a wave-function. This can be a system of ONE particle, two, three, or more, but on condition that we know exactly how it evolves, and it always remains a well-defined wave-function. (It even can be even a superposition of energy eigenstates, i.e. the energy not unique.)
Now, if this system interacts with another system, consisting in an undefined number of particles, and whose wave-function we cannot write (because we cannot follow the evolution of this system), e.g. a bath of particles, a macroscopic apparatus, the environment, etc., the system under observation becomes, for us, DECOHERED.
That means, if initially we could write it as,
$$|\Psi\rangle = \sum C_i |\Psi_i \rangle ,$$
the phases of the constants $C_i$ become undefined. The wave-function transforms into a mixture.
You may ask whether the decoherence is an effect of our inability to follow the evolution of a complex system. IT MAY BE. We cannot give a definite answer, because indeed, we cannot follow it and cannot say what would have happened if we could follow.