an abt is similar to an octree.
what it does:
it recursively splits the geometry along an axis aligned splitting plane. this plane doesn't simply get placed at the center of the bounding box of each node but its placement somehow gets adapted/optimized (so that both sides have the same amount of polygons or so that empty space gets handled efficiently but only jcl knows the exact criteria of his implementation

).
this tree of geometry nodes then can be used for fast frustum culling and such things. it works with any polygon geometry and is much better for modern gpus since it is much coarser than old quake-style bsp.
<edit> here i found a much more detailed explanation:
http://www.gamedev.net/community/forums/topic.asp?topic_id=123169. this thread is from 2002. read what he says about quake-style bsp!

</edit>
with quake-style bsp the geometry gets split recursively too but with non-axis aligned splitting planes. the algorithm is much more complicated and i don't know the details but we all know the disadvantages. convex blocks, long compile time, bad for the gpu since it is way too fine grained (1 polygon leaf nodes),...