What we see in a scene may not be what the viewer of our images takes away from the print. It is therefore important to use our skill to direct the viewer to how we want them to "read" the image, where to look first, and what to concentrate on.
We can choose subject (or at least an example of this subject) which tends to stand out from the surrounding and background. We can wait for or supply lighting that emphasizes what we feel is important. Often however, this kind of viewer direction doesn't come to us until we are editing the image (even though it would have been better to consider this from the start).
A light object against a dark background stands out, as does a dark object against light, though perhaps not to quite the same degree. A blurred background helps emphasize the important while a cluttered fairly sharp background is a nightmare for emphasizing the important. However, by reducing the contrast in the less important parts of the image, while also darkening them, we stand good chance of emphasizing the important.
While deliberately blurring a large background (or foreground) often looks artifical, done subtly or in small areas it can be useful. More importantly, you could deliberately only add sharpening to the important elements of the image. Of course, it would have been better in the first place to have given yourself a choice, one shot at f16, another at 5.6 so you could choose the best effect for this image.
Occasionally a very odd looking Curve adjustment layer can be very effective ad de-emphasizing parts of the image. The same curve might look horribly unnatural for another image but works for this one - you just have to experiment.
Local contrast enhancement is exactly what you don't probably want to do to the things you don't want emphasized, but doing it to the important parts can be very helpful. By the same token though, using local contrast to lighten shadows and tone down highlights can, if carefully applied, reduce distraction from bright highlights and deep shadows, even though there is more texture there.
Careful tonal adjustment of the important objects can render them more three dimensional and therefore more noticable.
We often use lines in our compositions - a fallen log, a linear shadow, or whatever to direct the eye of the viewer from one part of the image to the next. Sometimes the "object" used isn't obvious enough and lightening the whole thing can be helpful or even better is to use Dodge Highlights to highlight part of the object to emphasize the line. Adding highlights to the important elements can really help them stand out, without having to change the overall tone of the object. Dodge Highlights, if done well, can create highlights where there were none before.
The goal of all this image manipulation must be that the viewer isn't even aware that it ever happened. Too often, things are taken too far - if a little bit of dodging or burning is good, then a lot must be wonderful - well, no, it doesn't work that way. The viewer doesn't want to feel manipulated, doesn't need to have a sense of fakery, Not all skies have to look like the end of the world is nigh.