A sliver is basically a tiny degenerate geometry in the micro/nanometer scale that's basically the result of ambiguous surface intersections. Basically, if you put two say, cylindrical surfaces against each other in NURBS form, floating point noise would generate these microscopic geometric noises, and a lot of what commercial kernel does is they use what they call "healing" operations to clean up those bad microscopic geometries from the models they generate.
Aetheris took a very obvious approach that not many have seemed to tried before: It throws an error when an operation that may create ambiguous intersections and refuses to materialize bad geometry in the first place, which is not really possible to do with traditional NURBS based kernels, whereas Aetheris can because it is analytical first.
You see slivers in 2D spatial operations as well. Imagine that you have two parcels represented as polygons that don’t perfectly spatially intersect. If you perform a boolean operation to, say, compute the union of these two polygons into a single one, any microscopic difference between the two boundaries below a certain tolerance (like 0.001 square meters) will manifest itself as tiny gaps and slivers. Most GIS engines will merge the two polygons appropriately beyond that tolerance (this is a way simpler problem in 2D space!) but if the data is bad enough you’ll definitely see it.
While this is technically correct behavior, users will interpret that as your software not being able to do something - or as a bug (because it works on one drawing but not another).