They [heralds] presided at the weddings and funerals of armigerous families, so as to keep straight the implications of those generational comings and goings for family pedigrees. (Tittler, Robert., Portraits, Painters, and Publics in Provincial England (1540-1640), p104)
What does "the implications" means in here? Is possible it refers to a genealogical concept? Honestly, I do not understand its semantic relation with whole of the sentence.