In simple terms, bokeh relates to how out-of-focus details are rendered. However, bokeh cannot be measured, and is only perceived and evaluated subjectively, usually in terms of "good" or "bad" bokeh. A creamy fuzziness is generally regarded as "good" bokeh. This seems to be related to the way a lens tries to correct spherical and other aberrations, but in no clear nor predictable way. Bokeh is also unrelated to a lens' sharpness, contrast and resolution.

Bokeh is an incorrect transliteration of the Japanese word boke (boke), which translates to "unfocused". It has been reported by several sources that bokeh comes from the more common Japanese word boke, similarly read boke, which means "stupid", "confused" or "senile", but this is incorrect. The two words are not related. It is said that the spelling bokeh was introduced in order to suggest an approximately correct Japanese pronounciation to English speakers, but this simply violates the Japanese transliteration rules. It would be the same as insisting to write sakeh instead of sake, or animeh instead of anime. Nonetheless, the bokeh spelling is nowadays in common use as an English word, and I am using it as such.

Out-of-focus bright points rendered as disks, with a sharp outline brighter than the interior of the disk, seem to be the example of "bad" bokeh that comes closest to an objective, non-aesthetic judgement. This type of  "bad" bokeh seems to be present in over-corrected lenses. Lenses that are designed not to produce aberrations in the first place (as opposed to creating them first, and then correcting them with additional elements), instead, tend to produce uniformly lighted out-of-focus disks with a sharp outline. However, a "good" bokeh instead seems to require out-of-focus disks with a bright centre that fades gradually outwards (which implies that the lens does not correct spherical aberrations very well). To make things more confusing, some lenses display a "good" bokeh in one direction, relative to the plane of focus, and a "bad" bokeh in the opposite direction. Others may show a "bad" bokeh in both directions, but virtually no lens shows a "good" bokeh in both directions.

As a whole, the concept of bokeh seems to be as "fuzzy" and subjective as the fuzziness it is supposed to quantify. From a practical point of view, Murphy's law guarantees that "bad" bokeh in a picture will be on the side of the focal plane where it is least desirable, and that the lenses with the "best" bokeh for a given situation are those you don't have.

I am aware of only one attempt to relate bokeh to a measurable lens parameter: according to this explanation, a "better" bokeh results when the meridional and sagittal MTF functions of a lens are close to each other. This is likely to be true, but I am sure that bokeh does not depend on this factor alone.

Nikon makes two variable-bokeh lenses, a 135 mm and a 105 mm DC (= Defocus Control). They have an extra rotating ring near the front of the barrel that looks like a second aperture ring, but is graduated in aperture units first decreasing, then increasing again along the scale. "Defocus" is minimum at the centre of this scale, and grows towards either end. It works by moving internal elements back and forth.

Whether you should turn the defocus ring to the right or left depends on whether the unfocused parts of the picture lie mostly in the background or foreground, and on the effect you want to obtain. As a whole, the effect is not very marked, and you have to examine the pictures carefully to see the difference among the DC settings. DC does not affect the in-focus areas of the picture (and for this reason, most users of these lenses actually do not understand what it does). A by-product of varying the DC is that it makes the plane of focus slightly concave or convex, so you do see some slight differences in the in-focus areas near the edges of the picture, but this is only an accidental consequence, not the purpose of these lenses.

You may turn the defocus ring up to a setting that corresponds to the diaphragm aperture you are using, but you should not go beyond this value. If you do, the result is rather ugly aberrations. You can, however, use a lower setting (i.e., a setting closer to the centre of the ring).

You may also find reviews that assume the DC lenses are equivalent to soft-focus lenses. DC lenses definitely are not soft-focus, because they are very sharp in the plane of focus. As far as I am aware, these Nikkors are the only variable-bokeh lenses in existance.