Faceted schemes classify things by selecting properties from a vocabulary. The classic example is wines, where one classifies by selecting variety, region, grape, age, et cetera.
In other words, there are multiple orthogonal "dimensions" (such as variety, region, etc) and each dimension has a hierarchy (for instance, "France" might be a region, and "Bordeaux" might be a subregion of "France"). So, there are many parallel hierarchies (the "region" hierarchy, the "age" hierarchy, etc), and an item can be classifified in each hierarchy simultaineously.
A common alternative is to classify everything in a single hierarchy. For example, when classifying one's blog posts, one might first split them into work-related, holidays, and comedic, then subdivide holidays into Europe, Australasia, et cetera.
FacetedClassification is generally more flexible, but initially more complex to set up.