B.A Baracus has didly squat to do with the T-Buffer. In fact, CTO and general good egg at 3dfx, Gary Tarolli, was the architect responsible for their T-Buffer technology and hence the 'T' credit. But what is it?
A simple explanation is that 3dfx' T-Buffer technology is borrowed and modified from an expensive real-time rendering technique, the Accumulation Buffer that in turn was inspired by non-real-time techniques in ray tracing. With the Accumulation Buffer, each element is rendered and combined multiple times (usually 16 to 30 renderings of slightly different images) to get the layering of effects that creates the final composited image. While this could easily be accomplished in real time on a fridge-freezer sized, small country GOP priced, SGI Reality Engine (hundred's of thousands of dollars!), not too many of us have one of those at home reserved for playing games.
With its use of multiple buffers, the T-Buffer will work in a very similar fashion to an accumulation buffer but in real time on your PC. As most of the dramatic visual effect is achieved in the first four to eight 'layers', a close approximation of the Accumulation Buffer technique can be achieved in real time by cutting down on the number of repetitions, bypassing the accumulation step and also by applying particular effects to only a selected portion of an image instead of re-rendering the whole image to add effects to only one part. That is just what 3dfx proposes.
You have probably heard of anti-aliasing and motion blur. You may not be familiar with depth of field (DOF), soft shadows and reflection blur. What all these effects have in common (besides being too expensive to put into your PC) is that they are all variations on anti-aliasing.