To be more precise, why did the Nazis feel the need to tell the difference between a person who was for example 1/4 Jewish and a person who was 1/8? Considering how extreme they were couldn't they just consider anyone who had Jewish ancestry Jewish no matter how long ago their Jewish ancestor lived?
Records were not always easy to get, so they only required going back two generations. Just think about even today, could you find the official birth baptismal certificates of both your parents and all four of your grandparents? That's seven certificates. Now imagine they demanded to the 1/8 level. That would be 15 certificates, and go back about 80 years.
Everybody was guilty until proven innocent, so you better have your papers. Once you prove your "blood", then you get a card showing your Aryan blood level. No card, you go to camp.
EDIT:
change "birth" to "baptismal"