We have previously discussed that it is by no means necessary to have witchcraft ancestry to become a witch. To put this in terms of pop culture, the fact that Hermione Granger, a Muggle, was first in her class at Hogwarts, is certainly a possibility in real life, meaning that any individual can move their way through the Coven. But the notion of lineage cannot be readily discarded.
It is very important in various senses. First, an individual born to Practitioners is exposed to Occultist ideas and Rituals at a very early age, rather than coming across these ideas in a theoretical book during their teenage or adult years. Second, an individual with Practitioner relatives is more likely to have a strong sense of pride in their beliefs. It is a sort of coat of arms, and this individual descended from a line of those who have studied and followed the Craft is unlikely to compromise their beliefs easily.