- Primogen appears to be a constructed word specifically for use in Vampire: the Masquerade. It likely was derived from primo- ("first") and -gen (Greek genes, "born"). Therefore primogen = firstborn.
Primogen are, at least in theory (although practice certainly differs) the representatives of their clans to the prince of a city in Camarilla-controlled cities. As with many Camarilla offices, the office predates the Camarilla and was also in common use in the Dark Ages.
The term is both singular and plural, and refers to both individual representatives and to the Primogen council as a whole.
Theoretically, a primogen is the oldest vampire of his clan, and serves as a representative and voice for the clan in city affairs. In the modern era, the officeholder is usually decided within the clan proper by voting, violence or someone higher up giving the orders, rather than simply comparing ages. Primogen traditionally make up a council that is the second most powerful institution in the city after the Princedom.
The power of the primogen varies with the power of the vampires that make it up: in some cities they are a rubber stamp for the prince, while in other cities they manage all affairs.