Hydrogen adsorption in high surface area nanoporous coordination polymers has attracted a great deal of interest in recent years due to the potential applications in energy storage. Here we present combined inelastic neutron scattering measurements and detailed first-principles calculations aimed at unraveling the nature of hydrogen adsorption in HKUST-1 (Cu3(1,3,5-benzenetricarboxylate)2), a metal-organic framework (MOF) with unsaturated metal centers. We reveal that, in this system, the major contribution to the overall binding comes from the classical Coulomb interaction which is not screened due to the open metal site; this explains the relatively high binding energies and short H2-metal distances observed in MOFs with exposed metal sites as compared to traditional ones. Despite the short distances, there is no indication of an elongation of the H-H bond for the bound H2 molecule at the metal site. We find that both the phonon and rotational energy levels of the hydrogen molecule are closely similar, making the interpretation of the inelastic neutron scattering data difficult. Finally, we show that the orientation of H2 has a surprisingly large effect on the binding potential, reducing the classical binding energy by almost 30%. The implication of these results for the development of MOF materials for better hydrogen storage is discussed.