Lineage is the Kindred term for their direct blood relation to fellow clan members. The line of their sire and of their sire's Sire and so on. Clan Ventrue are among the main ones that hold to this the most. Upon the presentation of a newly created vampire, the fledgling is tasked with not only remembering the Traditions and stating them, they are also tasked with speaking their line of Lineage back as far as it is known. They will also stress the connection to any famous members of the bloodline. With most clans, their Lineage often grants prestige and boons or opens doors that most newly created Kindred would not have a chance to go through early in their unlife.
With older Kindred, it is often used also to depict what Clan a being may be from. "Do not trust Maltese, he is of the Lineage the Brujah, nothing more then rabble if you ask me."