A term borrowed from the Japanese, pronounced with short vowels. (ie: more like French pronunciation - bo-ké - versus long English diphthongs - bow-kay.) Essentially bokeh, which is Japanese for blurring, refers to the quality of out of focus areas of a picture. Bokeh can be important for portraiture - you want out of focus areas behind the subject to be smooth and as non-distracting as possible. Highly patterned or sharp-edged areas don’t look as good.
Many factors in the design of the lens influence bokeh, which is in turn a pretty subjective concept. For example, lenses with very few aperture diaphragm leaves (perhaps 5) tend result in pentagonal out of focus highlights. Lenses with more aperture leaves (7 or 8 or more) tend to result in rounder out of focus highlights. This can affect bokeh under certain circumstances, though is by no means a guarantee of good bokeh.
Mirror lenses are notorious for bad bokeh - they have annular (ring or doughnut shaped) out of focus highlights and fine detail lines tend to appear as double lines. This form of bokeh, “cross-eyed” or “ni-sen bokeh,” (Japanese for two line bokeh) is one in which detail lines appear as blurry double lines.