This annotation property links a subproperty of prov:wasInfluencedBy with the subclass of prov:Influence and the qualifying property that are used to qualify it.
prov:wasGeneratedBy prov:qualifiedForm prov:qualifiedGeneration, prov:Generation .
Then this unqualified assertion:
:entity1 prov:wasGeneratedBy :activity1 .
can be qualified by adding:
:entity1 prov:qualifiedGeneration :entity1Gen .
a prov:Generation, prov:Influence;
:customValue 1337 .
Note how the value of the unqualified influence (prov:wasGeneratedBy :activity1) is mirrored as the value of the prov:activity (or prov:entity, or prov:agent) property on the influence class.