It is the standard secondary-recovery method. The extra oil comes from two places: less gas breaking out of solution because pressure is held, and oil displaced from rock the water actually sweeps. Residual oil in the swept rock, and oil in rock the water never reaches, are both left behind.
How well it works depends on the mobility ratio, the heterogeneity of the reservoir, and where the injectors and producers sit. A flood with an unfavorable mobility ratio fingers through the oil. Polymer is sometimes added to the injection water to raise its viscosity and slow that fingering. Water injection for disposal, with no intention of sweeping oil, is not a waterflood.