The word comes from the Japanese boke, meaning haze or blur. Crucially, bokeh is a quality judgement, not a quantity. Two lenses can render the same amount of background blur and have completely different bokeh: one creamy and smooth, the other busy and nervous.
Most of the character comes from the aperture blades. A lens with rounded blades turns out-of-focus highlights into soft circles; one with straight blades turns them into pentagons or heptagons. Optical corrections matter too — some designs produce bright-rimmed circles known as onion-ring or soap-bubble bokeh, prized by some shooters and avoided by others.
Good bokeh does invisible work. It keeps the background from competing with the subject, so the eye stays where you put it. Bad bokeh does the opposite: harsh double-edged shapes and jittery highlights drag attention backwards. This is why fast primes with well-regarded rendering hold their value long after their sharpness has been surpassed.