The original aural exciter by Aphex which at first you couldn't buy at all but rented and paid for by the finished minute of master resulting from its use, or something like that, apparently added an adjustable amount of even order harmonics to the signal, much as some tube amps do. The BBE claimed to have a similar effect but achieved it, if I remember correctly, by bringing the "presence range" (2-4 kHz, roughly) forward by default, by delaying all the other frequencies somewhat. I read this in their advertising copy back in 1990 or so, hope I have it right.
The CBC, Canada's national broadcasting corporation, bought a lot of BBEs, I understand, but replaced them around 1991 with "spl Vitalizers" - up-market German devices which did a similar thing, but using different techniques (totally proprietary, of course!). These devices, of which I still own one - I had a BBE before it, were much more adjustable and were capable of affecting stereo width as well as bass quality. In fact they said it was aimed at addressing the two most common problems encountered in mastering - lack of clarity (muddy or veiled presence range) and flabby bass.
All of these devices were client pleasers in that the client almost always liked the effect but the danger, as you might imagine, was over-use. They could improve a pop mix if used in moderation, but were often over-used and often were not necessary at all. If over-used, the result was fatiguing.
