Yttria (Y₂O₃) is a well-known ceramic material extensively used in industry. We report new neutron inelastic scattering measurement of the phonon density of states (PDOS) and lattice dynamic calculations using the ab-initio density functional theory and interatomic potential model, which are found to be in good agreement with each other. The model is then used in extensive free-energy calculation to understand the stability of various phases as a function of pressure and temperature. We find that one of the Y-O bonds shows a very large compression with increasing pressure, involving change of coordination around the Y atoms. This seems to provide the mechanism of the transition from the monoclinic phase to the hexagonal phase at the high pressure. We find that this transition is displacive in nature, and we also identify how the change of coordination affects the phonon spectra of the various phases.