Bokeh describes the rendition of out-of-focus points of light.
Bokeh is different from sharpness. Sharpness is what happens at the point of best focus. Bokeh is what happens away from the point of best focus.
Bokeh describes the appearance, or "feel," of out-of-focus areas. Bokeh is not how far something is out-of-focus, bokeh is the character of whatever blur is there.
Unfortunately good bokeh doesn't happen automatically in lens design. Perfect lenses render out-of-focus points of light as circles with sharp edges. Ideal bokeh would render each of these points as blurs, not hard-edged circles. Mathematicians would say the intensity distribution of the blur circles are rectangular in perfect lenses, and good bokeh would prefer a Gaussian distribution. This is one area in which physics doesn't mirror what we want artistically.
Differing amounts of spherical aberration alter how lenses render out-of-focus points of light, and thus their bokeh. The word "bokeh" comes from the Japanese word "boke" (pronounced bo-keh) which literally means fuzziness or dizziness.
A technically perfect lens has no spherical aberration. Therefore a perfect lens focuses all points of light as cones of light behind the lens. The image is in focus if the film is exactly where the cone reaches its finest point. The better the lens, the tinier this point gets.