When a camera moves during an exposure, a point of light can smear across multiple pixels. Optical image stabilization tries to keep that image nearly still on the sensor while the shutter is open.
Measuring camera shake
Sensors detect movement of the camera or lens. A controller then shifts a lens element, the image sensor, or both in a direction that counters the measured shake. The correction happens continuously and has a finite range and response speed. This can help a handheld photograph at a slower shutter speed.
What it cannot freeze
Stabilization cannot stop a person, animal or vehicle from moving within the scene. It also cannot recover detail that was never focused correctly. For a moving subject, a sufficiently fast exposure may still be needed. The distinction matters: stabilizing the camera’s light path is different from changing the sensor’s ability to capture photons.
Related: how a camera sensor converts photons into pixels.