'Bokeh' is a Japanese word used to describe the quality of out-of-focus areas in a photograph. Points of light which are out of focus appear as discs, and the more perfectly circular and evenly illuminated these discs are, the better the bokeh is considered to be.
Bokeh is dependent on the optical design of the lens and the number of aperture blades in the lens diaphgram mechanism. The closer the aperture is to circular, the better the bokeh. Bokeh becomes particularly important when you're using larger-format cameras, longer focal length lenses and wider lens apertures - in other words, any time when your photographs will have shallow depth of field.
You may never notice any difference in bokeh between one image and another, and you may feel the whole idea is a lot of pretentious rot, but there are instances where differences are obvious. Users of old-fashioned catadioptric telephoto lenses will be familiar with their characteristic doughnut-shaped highlights in out-of-focus areas, and it's possible to spot the hexagonal/pentagonal shapes of defocussed highlights created by many older lenses.
This is why lens makers quote the number of diaphragm blades in their lenses. The greater the number the better, in theory, the bokeh.
Opinions about the correct pronunciation vary, by the way. Most seem to think it should be pronounced with short vowel sounds as in bo-ke ('bo' as in 'box' and 'ke' as in 'kettle').