Sharpening is an image manipulation technique which increases apparent sharpness by increasing local contrast
An edge looks sharper if the edge contrast is higher. Sharpening steepens edge contrast by making the dark side of the edge darker and the bright side brighter. Unfortunately this causes halos along those edges, hence sharpening has to be done very carefully.
Most common sharpening techniques are based on unsharp masking. However, there are more sophisticated sharpening techniques that f.e. don't apply sharpening to already sharp or to high contrast edges. The most advanced technique, deconvolution, tries to mathematically remove the blurring, which is perfectly possible if the exact way the image was blurred (convoluted) is known. An example how to use the Wiener Filter contained in PanoTools for deconvolution is Helmut Dersch's attempt to Restorate Star Trail Images: