For subschemes in projective space liaison arises from the geometric notion of
linkage. Roughly speaking, two subschemes are directly linked if their union is
a complete intersection. The equivalence relation generated by linkage is called
liaison. One can also define a finer equivalence relation called biliaison (or even
liaison): two subschemes are in the same biliaison class if they are related to each
other by an even number of direct links. Thus, in some sense, a biliaison class is
"half" of a liaison class. It turns out that biliaison classes are the right object to
study in the context of liaison.
