We provide a thorough study of a carbon divacancy, a fundamental but almost unexplored point defect in graphene. Low temperature scanning tunneling microscopy (STM) imaging of irradiated graphene on different substrates enabled us to identify a common two-fold symmetry point defect. Our first principles calculations reveal that the structure of this type of defect accommodates two adjacent missing atoms in a rearranged atomic network formed by two pentagons and one octagon, with no dangling bonds. Scanning tunneling spectroscopy (STS) measurements on divacancies generated in nearly ideal graphene show an electronic spectrum dominated by an empty-states resonance, which is ascribed to a spin-degenerated nearly flat band of $pi$-electron nature. While the calculated electronic structure rules out the formation of a magnetic moment around the divacancy, the generation of an electronic resonance near the Fermi level, reveals divacancies as key point defects for tuning electron transport properties in graphene systems.