A simple example is white balance. The sensor doesn't know anything about it, but typical postprocessing makes both a 2700K incandescent and a 5700K strobe look white. A photographer might prefer to make the incandescent lights look more yellow. There's a white balance setting in the camera to do that when taking the picture, but it's a lot easier to get it perfect later in front of a large color-calibrated display than in the field.
Another example is dealing with a scene containing a lot of dynamic range, such as direct sunlight and dark shadows. The camera's sensor can capture a greater range of brightness than a computer screen can display or a printer can represent, so a photographer might prefer to delay decisions about what's dark grey with some details and what's clipped to black.