What histograms do show us it the range of values across the image. If I see the histogram has values of 255, we know we have blown highlights, and with perhaps the exception of specular highlights, this is generally not something we want in images. The inverse of this problem is black values of 0; which in my view is not quite as much of an issue, so long as there aren't too many of them.
When I look at an image that has whites, but the histogram shows grays, to me this is a problem. For some strange reason I have always thought (and have been taught), whites should actually look white. The same at the other side of the histogram; we see things that should be black, but we see grays instead. This too is a problem, because to my little mind (and again this is consistent with what I was taught), blacks should look black.
One of the problems I've always had with Lightroom is that setting the black point and white point is relatively easy, but changing the mid-point (gamma) value in not intuitive. This adjustment is far easier in Photoshop, with the levels adjustment.
If I work in either Lightroom or Adobe Camera Raw (the user interface with these two pieces of software are different, but the underlying engine is identical), I can follow these rules and get an image that is quite similar to Kathy's (softness), but am able to preserve some of the details that are lost in her image (mostly where the trees and sky meet and to a lesser extent in the water).
My re-edit
Kathy's original edit
If you open these two images in Lightbox and use the back / forward keys you can see the differences in the edits, and they are quite subtle.