The structure of the tetrahedral backbone and the nature and time scale of the temperature-dependent structural changes in binary Ge-Se glasses and supercooled liquids with <= 33.33 atom % Ge have been investigated using ambient and high-temperature Raman spectroscopy. The composition dependence of the relative fractions of edge- and corner-shared GeSe4 tetrahedra and that of the characteristic mean vibrational frequencies of these structural units are shown to be consistent with a structural model for these glasses based on a random interconnection between GeSe4 tetrahedra and Se-Se chain fragments. The most prominent temperature-dependent structural change in the Ge20Se80 glass and supercooled liquid involves progressive conversion of the edge-shared GeSe4 tetrahedra into corner-shared tetrahedra, upon lowering of temperature. The time scale of this tetrahedral conversion "reaction" corresponds well with those of enthalpy and shear relaxation near glass transition. Moreover, the temperature dependence of this GeSe4 tetrahedral speciation is shown to be the most important source for the production of configurational entropy in this supercooled liquid near the glass-transition range, signifying a direct link between structural relaxation, configurational entropy, and viscous flow.