Like the CIELAB Delta E metric, the S-CIELAB metric is a "perceptual color fidelity" metric. It measures how accurate the reproduction of a color is to the original when viewed by a human observer. The CIELAB metric is suitable for measuring color difference of large uniform color targets. The S-CIELAB metric extends the CIELAB Delta E metric to color images.
Color discrimination is determined by a lot of factors, such as the cone sensitivity of the eye, the ambient illumination, the spatial pattern of the targets, etc. The effects of some of these factors on color sensitivity are better understood than others. To learn the basics (and advances) about color science and vision in general, check out the book Foundations of Vision, written by Brian Wandell.
One of the most widely used perceptual color fidelity metric is the Delta E metric, given as part of the CIE L*a*b* standard color space specification. To measure perceptual difference between two lights using this metric, the spectral power distribution of the two lights are first converted to XYZ representations, which reflect (within a linear transformation) the spectral power sensitivities of the three cones on the human retina. Then, the XYZ values are transformed into an L*a*b* space, in which equal distance is supposed to correspond to equal perceptual difference (a "perceptually uniform" space). Then, the perceptual difference between the two targets can be calculated by taking the Euclidean distance of the two in this L*a*b* space. The difference is expressed in "Delta E" units. One Delta E unit represents approximately the threshold detection level of the color difference.
The CIE L*a*b* Delta E metric is intended to be used on large uniform color targets (at least 2° visual angle in size).
Color discrimination and appearance is a function of spatial pattern. In general, as the spatial frequency of the target goes up (finer variations in space), color differences become harder to see, especially differences along the blue-yellow color direction. This result came from many studies, including Poirson & Wandell (1993, 1996), Kelly (1983), etc.
So, if we want to apply the CIE L*a*b* Delta E metric to color images, the spatial patterns of the image have to be taken into account. The goal of the S-CIELAB metric is to add a spatial pre-processing step to the standard CIELAB Delta E metric to account for the spatial-color sensitivity of the human eye.