From Wikipedia: "In heraldry, an armiger is a person entitled to use a heraldic achievement (e.g., bear arms, an "armour-bearer") either by hereditary right, grant, matriculation, or assumption of arms. Such a person is said to be armigerous."
Usage in the Republic
In order to become recognized as an Armiger, one must be granted this right either directly through a Grant of Arms or an Award of Arms which is typically tied to one of the aforementioned positions or as its own reward. The granting or awarding of arms will accompany the awarding of the titles of nobility or position if it is to be so and would be considered an armigerous award. There may be times where a title or position is awarded as non-armigerous.
In order to obtain a heraldic achievement, an armiger will consult with the College of Arms via a consulting Herald in order to register their arms. Heralds conduct consultations of arms in accordance with the Law of Heraldic Arms as published by the College of Arms.
Book of Nobility
The Libro d'Oro lists the nobility of the Republic and includes the direct and immediate hereditary Armigers as well as cadet Armigers who hold titles as offshoots of the main line of inheritance.