Bokeh is a Japanese word which means "stupid" or "idiotic" or "confused, unclear". So, in photographic sense, it is the "out of focus" areas in the picture. Can be in front of subject or behind the subject, assuming the subject is question is correctly focussed.
I think the serious Japanese photographers were the first to value "good" bokeh. Japanese lens reviews give alot of emphasis on the bokeh characteristics. Essentially, good bokeh gives a nice feeling to the viewers and bad bokeh is distracting to viewers. This is pretty obvious if you place 2 similar pictures side by side taken by different lenses using the same large F-stop. Good bokeh is defined by it's smoothness, shape, gentle transition. You can read more about this from the links provided by the other posters.
Technically, the bokeh characteristics is affected by the lens design and the shape of the aperture blades. The more circular the aperture the nicer the bokeh. Among the Japanese, Minolta appears to more consistent in producing good bokeh in their lens design and were among the earliest to promote circular aperture blades.
Each of the major manufacturers typically will have some lens in their lineup that has good bokeh, and others that are so-so or just plain terrible. Sometimes a lens is designed to give better sharpness at the expense of bokeh or vis versa. Sometimes background bokeh is great, but foreground bokeh is so-so.
It is said that some of the Leica lenses, particularly the M series, gives very nice bokeh and still has great sharpness, flat field, contrast and color, and therefore very much desired by the Japanese photographers. These "ideal lens" costs an arm and a leg. Cheaper M type lens alternatives with nice bokeh are offered by Voigtlander Cosina.
If your shooting style is frequently using large aperture or wide open you will value lens with great bokeh. If you prefer everything in the picture to pin sharp, such as wide angle landscape, then the bokeh is not important.
