It is the ultimate goal of this work to foster synergy between quantum chemistry and the flourishing field of quantum information theory. For this, we first translate quantum information concepts such as entanglement and correlation into the context of quantum chemical systems. In particular, we establish two conceptually distinct perspectives on correlation leading to a notion of orbital and particle correlation. We then demonstrate that particle correlation equals orbital correlation minimized with respect to all orbital reference bases. Accordingly, particle correlation resembles the minimal, thus intrinsic, complexity of many-electron wavefunctions while orbital correlation quantifies their complexity relative to a basis. We illustrate these novel concepts of intrinsic and extrinsic correlation complexity with analytic and numerical examples, which also demonstrates the crucial link between the two correlation pictures. Our results provide theoretical justification for the long-favored natural orbitals for simplifying electronic structures, and open new pathways for developing more efficient approaches towards the electron correlation problem.