The mixed-valent iridate Ba3InIr2O9 has been discussed as a promising candidate for quantum spin-liquid behavior. The compound exhibits Ir4.5+ ions in face-sharing IrO6 octahedra forming Ir2O9 dimers with three t(2g) holes per dimer. Our results establish Ba3InIr2O9 as a cluster Mott insulator. Strong intradimer hopping delocalizes the three t(2g) holes in quasimolecular dimer states while interdimer charge fluctuations are suppressed by Coulomb repulsion. The magnetism of Ba3InIr2O9 emerges from spin-orbit entangled quasimolecular moments with yet unexplored interactions, opening up a new route to unconventional magnetic properties of 5d compounds. Using single-crystal x-ray diffraction we find the monoclinic space group C2/c already at room temperature. Dielectric spectroscopy shows insulating behavior. Resonant inelastic x-ray scattering reveals a rich excitation spectrum below 1.5 eV with a sinusoidal dynamical structure factor that unambiguously demonstrates the quasimolecular character of the electronic states. Below 0.3 eV, we observe a series of excitations. According to exact diagonalization calculations, such low-energy excitations reflect the proximity of Ba3InIr2O9 to a hopping-induced phase transition based on the condensation of a quasimolecular spin-orbit exciton. The dimer ground state roughly hosts two holes in a bonding j = 1/2 orbital and the third hole in a bonding j = 3/2 orbital.