Within the wizarding world, Harry enjoys a particular sort of social privilege: not only is he The Boy Who Lived, he is also the son of James Potter, of the pure-blood Potter family. Due to his Muggle upbringing, Harry pays little notice to his own blood status, let alone anyone else's. However, wizarding genealogy indicates that the son of Muggle-born Lily Evans and nephew of decidedly unmagical Petunia may belong to an ancestral chain that goes back generations into pure-blood history. Though Rowling mentions James Potter's parents only in passing as a wealthy couple who had a child quite late in life, some clever fans have connected the dots and think they might know exactly who Mr. and Mrs. Potter are.
The Noble and Most Ancient House of Black exemplifies the most rabid sort of pure-blood family, the kind which kept an elaborate family tree of their exclusively magical lineage dating back to the Middle Ages, and disowned any sons or daughters considered to be "blood traitors." With their family motto of Toujours pur ("Always/Still pure"), the Blacks took cruel pride in burning off the names of such blood traitors from their family tree, preferring singed holes in the tapestry to an acknowledgment of any impurity. Just as the tree links the Black family to the Malfoys, the Weasleys, the Prewetts, and other pure-blood families by marriage, it may also provide a link to Harry Potter himself, by way of Dorea Black's marriage to Charles Potter. These two, fans believe, are none other than —Harry Potter's grandparents.
Secondary to this is the possibility that Charlus and Dorea's unnamed son was James's father, thereby making Dorea Black Harry's great-grandmother. Either of these possibilities suggests direct familial relationships between Harry and many of his loved ones: his wife Ginny may be his third cousin; his godfather Sirius his second cousin, twice removed; and Arthur Weasley, Andromeda Tonks, Bellatrix Lestrange, and Draco Malfoy various other forms of cousins. The third possibility is that Charlus Potter was a more distant relative of James Potter, leaving Harry as unentangled with the Noble House of Black as before—but without additional canonical information, each option is as likely as the next.