This is a type of HashTable with positive integer keys, used to store the output of stratifyByRank. If M is a module of vector fields and h=stratifyByRank(M) is the StratificationByRank object, then h#i is the radical ideal defining the set of points $p$ such that the generators of $M$ evaluated at $p$ span a subspace of dimension less than $i$.
These objects are primarily used by isFiniteStratification.
If M is a Lie algebra, then this gives some information about the 'orbits' or maximal integral submanifolds of the vector fields.
The object StratificationByRank is a type, with ancestor classes HashTable < Thing.