Here's an example.
First, let's look at the original image. This happens to be a short stack (3 frames). In an ideal world, the face of the fly would be at least as sharp as that nice section at the back of the thorax between the wings. But it isn't. The face is soft. We don't know why it's soft -- perhaps there's some issue with motion blur or maybe just missing focus -- but we'd like to do the best we can to improve it.
Here it is, the original image:

Now, jumping clear to the end, here's what we finally end up with:

At first glance, there's not a huge difference between those two images. That's OK, there's not supposed to be.
But here's a closer look at just the fly and its immediate surroundings:

If that side-by-side comparison doesn't illustrate the difference, then consider this flashing comparison. (It's animated GIF at 2 seconds per frame. If the animation is working right, then in the lower right corner you'll see a flashing "Sharper" watermark.)

How was the sharpening done?
Quite strongly! What's shown above is sharpened using a Photoshop Unsharp Mask (USM) at 130% with a radius of 0.7 pixels.
If that amount of sharpening is applied to the whole image, then areas that were already sharp get obviously oversharpened:

To keep this from happening, we can use layers and masking to apply the sharpening only to areas where it's not excessive and that we care about. Here is the layer and mask structure that I used. The mask itself is shown here using Photoshop's "rubylith" format, which can be reached by alt-shift-click on the mask icon or by simply hitting the backslash key "\". To generate the mask, I used Layer > Layer Mask > Hide All, then painted "white" on the mask using an appropriately sized brush with a slightly soft edge.

Many thanks to Martin for letting me use his Helina fly in this demonstration. Similar techniques can also be used to "push back" areas that are already soft but you'd like softer. See "Sharper subject, blurrier background" for discussion.
I hope this helps!
--Rik