In an unrelated thread, I recently showed an example that pictures can be made to appear more "sharp" to the human eye/brain by simple image processing operations, in particular "unsharp masking". I've received requests for further clarification per PM. Here, I'll give two examples with some explanations how things work in non-mathematical terms for the benefit of those who haven't heard about it yet.
(1) is a synthetic "original". (2) is an "unsharp" version of (1), created using a "Gaussian blur" filter.
Another way of describing the "blurriness" of the edges in (2) is that instead of an abrupt change of brightness, the change is spread out, creating a gentle transition. To restore "sharpness", one has therefore to make this transition less gentle or, in other words, the slope of brightness transition has to be increased.
The simplest way of making the brightness scale steeper is to increase the image contrast. This is demonstrated in (3). Unfortunately, there are two undesired effects: Firstly, the contrast is not only increased at the edges, but everywhere, and darker regions in the image "drown" in the shadows while brighter regions are "burnt out". Secondly, while the edge transitions are steeper, they now have to cover a wider range from the darker shadows to the burnt out highlights, and while the transition is steeper, the overall width of the transition is unchanged.
The solution is to increase contrast only at/near the edges. A distinguishing property of edges compared to other image elements is that the brightness changes on small length scales. Therefore, if we increase the contrast for image features on small length scales while leaving it unchanged for larger image features, the problem is partially solved.
The desired manipulation falls into a class of signal processing operations known as "high pass filters". "Unsharp masking" is a family of high pass filters. (Note that I wrote "family" - "unsharp masking" by itself is not a well defined operation, and different programs may do somewhat different things.)
Typically, "unsharp masking" filters have at least two parameters: one is commonly called "radius" and specifies the scale (size) that determines whether image features are "large" (and to be left alone) or "small" (and to be boosted). The second parameter (often called "amount") specifies how much the small scale contrast is boosted.
In (4), image (2) was subjected to an "unsharp masking" filter with a "radius" of a few pixels. This markedly increases the edge contrast (or "acutance"), while leaving the overall tonal range unaffected. (4) looks visually "sharper" than (2). There are, however some artefacts: The increased contrast near the edges results in brighter "halos" on the bright side of the edge, and in darker "halos" on the dark side of the edge. (In signal processing, this effect is called "ringing.) Using the unsharp mask filter therefore requires a compromise between "better sharpness" and "less artefacts". The "best" compromise depends solely on the taste of the viewer.
Another way to make dull pictures more "spiffy" is to enhance the contrast of intermediate sized features. This is shown in the following example:
In the original image (A), the gray "blobs" don't stand out very well against the background. (The grayscale background could represent e.g. a transition from bright sunlight to a shady area.) Again, one could increase the global image contrast, but this would result in blown out highlights and "drowned" shadows.
In (B), the "local contrast" has been enhanced by unsharp masking. Since the "blobs" are of intermediate size, a intermediate feature size (radius) parameter was chosen for the filter. Similar artefacts (halos) as before are visible, too. (C) is the same as (B), except the (perfectly sharp) edges of the "blobs" have been exaggerated using unsharp masking with a small scale parameter (radius).
These techniques are not new inventions. In fact the term "unsharp masking" is a carryover from film days. By overlaying a picture with an out-of-focus negative of itself, large-scale contrast is reduced while small-scale contrast is unaffected. This is not identical, but mathematically very similar to what the computer USM filter does.
Also, there is an "edge effect" in film development that adds acutance (i.e. exaggerates edges or small-scale features) in much the same way as the computer version. In light of the latter, some image manipulation can hardly be counted as "cheating" - traditional photography does it all the time, whether the photographer wants it (or even knows about it) or not!
Finally, I should point out that in some circumstances, it is possible to create a "sharp" version of a blurred image without introducing artefacts. This requires however a detailed knowledge of the blurriness characteristics, which makes it impractical in general photography (for scientific image processing, it's an entirely different matter).
I'd also warn to take some explanations too literally. This forum is not the right place (and I don't have the time) to write a scientifically precise textbook .