Raman scattering phonon data of the quasi-two-dimensional quantum spin system (CuCl)LaNb2O7 are used to derive an effective structural model that may serve as a basis for its unconventional magnetic properties. Furthermore, a rich spectrum of magnetic excitations is observed, including quasielastic energy density fluctuations and finite energy bound states. These modes are the key to understand (CuCl)LaNb2O7 as a system with strong interactions between well-localized triplet excitations based on a pronounced competition of magnetic exchange.