The median filter is typically used to reduce noise in an image. It replaces each pixel with the median value of neighboring pixels. The median filter (unlike the blur filter) has the effect of reducing noise in an image while preserving edges. It is highly effective in removing impulse (speckles or salt and pepper) noise.
A technique that may have merit for some images involves running a median filter (to remove noise) and subsequently sharpening the image (so the noise is not sharpened).