Regularization does precisely a (edge-aware) smoothing of the curve. If you use the tone equaliser to compress the histogram, then increasing regularization will help preserving local contrast. However, if you use the equaliser to stretch the histogram (i.e. pull shadows and/or push highlights), then increasing the regularization value will counter that effect. As usual, a (short) video is worth a thousand words:
Hope this clarifies…
then I can try to come up with a label or help text.
suggestions are more than welcome! 