We present a first-principles study of the nature of the binding of a c(2x2)-CO overlayer on Ag(001) and of the origin of CO-CO interactions upon adsorption. Electronic structural changes induced by molecular adsorption provide an interpretation for earlier X-ray photoemission valence band spectra of CO/Ag(001). Our results establish that CO chemisorbs on clean 9 Ag(001) and follows the Blyholder model of donation and back-donation between CO and metal orbitals. We analyze the origin of the dispersion of the C-O stretch mode and attest that it is caused by the metal-CO coupling. Specifically, the coupling of CO to Ag,, although the weakest of those between it and transition and other noble metals, greatly enhances the intermolecular force constants. We also find that the response of the charge density around CO is much stronger and of longer range when the molecule stretches than when it rigidly vibrates against the surface. This difference explains why the C-O stretch mode disperses while the Ag-CO stretch mode does not.