Galaxies evolve under the influence of gas flows between their interstellar medium and their surrounding gaseous halos known as the circumgalactic medium (CGM). The CGM is a major reservoir of galactic baryons and metals, and plays a key role in the long cycles of accretion, feedback, and recycling of gas that drive star formation. In order to fully understand the physical processes at work within galaxies, it is therefore essential to have a firm understanding of the composition, structure, kinematics, thermodynamics, and evolution of the CGM. In this white paper we outline connections between the CGM and galactic star formation histories, internal kinematics, chemical evolution, quenching, satellite evolution, dark matter halo occupation, and the reionization of the larger-scale intergalactic medium in light of the advances that will be made on these topics in the 2020s. We argue that, in the next decade, fundamental progress on all of these major issues depends critically on improved empirical characterization and theoretical understanding of the CGM. In particular, we discuss how future advances in spatially-resolved CGM observations at high spectral resolution, broader characterization of the CGM across galaxy mass and redshift, and expected breakthroughs in cosmological hydrodynamic simulations will help resolve these major problems in galaxy evolution.