We show that the success of reduced density-matrix functional theory in describing molecular dissociation lies in the flexibility provided by fractional occupation numbers while the role of the natural orbitals is minor. By their definition, the natural orbitals and occupation numbers are the eigenfunctions and eigenvalues of the one-body reduced density matrix. This raises the question to which extend one can assign a physical interpretation to them, e.g. if the degeneracies in the occupation numbers reflect the symmetries of the system or if an excitation can be described by simply changing the occupations of the ground-state natural orbitals. We use exactly solvable model systems to investigate the suitability of natural orbitals as a basis for describing many-body excitations. We analyze to which extend the natural orbitals describe both bound as well as ionized excited states and show that depending on the specifics of the excited state the ground-state natural orbitals yield a good approximation or not.