Blood Preference (or Blood Affinity as it is called in the anime) is the preferred blood that a vampire will want to drink from humans. A blood preference is determined when a vampire reaches maturity, gains their fangs, and drinks blood for the first time. Depending on the preference, drinking blood (or giving blood, in the case of Karin) has different effects within humans (Example: Ren's blood preference being stress causes the women he bites to be more carefree and beautiful than they were before he bit them.)
In both the manga and anime, Karin's mother and father both seem to be surprised at the fact that their strange daughter was able to develop a blood preference herself, even though she didn't drink blood like the rest of them. The fact that this happened shows that even vampires that are born under rare or otherwise ridiculed circumstances can develop blood preferences like a normal vampire. This is probably due to the fact that Springs of Psyche (which they didn't know their eldest daughter was until later in the manga) don't appear unless the vampire race is struggling.