Really, this had to be the second entry, didn’t it?
But my Ilford Manual of Photography, 5th Edition, was absolutely no help: it just wasn’t a thing in 1968, and there’s not even a mention of differential focus in the index.
What is it? It’s the quality of the out of focusness of a background, and can be good or bad. Good Bokeh is described as soft and creamy, with smooth transitions between areas: bad Bokeh involves patterns appearing, or some features not fading away.
I’ve been researching this a bit, and I haven’t managed to find any lenses in my (reasonably extensive) collection that has notably poor Bokeh. After consulting banehawi, whose in-depth knowledge of cameras and lenses is amazing, I have experimented with a Helios lens from my elderly Zenit B.
Most of the time, it gives a nice look to out-of-focus backgrounds, but just occasionally, it can be distracting when the background patterns interact with the Bokeh – rather like the way that individual sensor sites can react with a tartan pattern to give Moiré patterns. Or the quality of the blur can just be a bit annoying...
Contrast this with the creamy and dreamy look that current wide-aperture lenses give: and this quality isn’t confined to the likes of Sony G-Master lenses and the Sigma Art range. Modern designs from Samyang also provide the look (I have a 135mm f/2 manual focus lens, and have played with 85mm and 50mm f/1.4 AF lenses that belong to my daughter-in-law). Please post pictures and names of lenses that you have found particularly good below.
The bottom line, though, is that if you like the look that a lens gives, use it! Like everything else in photography, theory has to bow to beautiful results.