D.B. Cooper 
, Mar 26, 2009; 01:25 a.m.
Luminance can mean a couple of things: color luminance adjustment (part of HSL, or Hue, Saturation, Luminance) or luminance noise reduction.
In color adjustment, 'Luminance' is the relative brightness of a color range. If you're playing with color adjustments, and there's little or none of that color in the image, nothing apparent will happen when you move the luminance slider. Try choosing another color that's more prominent in the image and try again.
The 'Luminance' control in digital noise reduction reduces luminance noise. It's very difficult to see any effect from this adjustment on a monitor, when viewing an entire image. If you zoom in (1:1 or more) to an area of the image that has good potential for digital noise (e.g shadow areas, darker bit of a sky), you should see the 'graininess' reduce and the area look smoother as the luminance slider is moved. Decreasing luminance noise can reduce image sharpness depending on how much noise reduction is applied, but that's another matter.