The Materials (マテリアル Materiaru) are primary units of the Automatic Defense System and (aside from possibly Reinforce) programs of the "Eternal Ring" of the Unbreakable Dark (U-D) System in the portable continuity. They were (aside from possibly Reinforce) initially one of the constituent programs along with U-D of the Tome of the Purple Sky, which was later added to the Tome of the Night Sky in an attempt to control the U-D. After Nanoha and Fate refuse to seal Reinforce and the Darkness of the Book of Darkness wakes, they are spawned by it as mages and given the powers and appearance of Nanoha, Fate and Hayate Yagami.
The nature of the Materials is similar to that of the Wolkenritter, and their existence can slightly be felt by Reinforce in the past. However, they were not materialized until the Defense Program was destroyed. Each of their materialized forms is a copy of one of the mages who defeated the Defense Program.
In The Battle of Aces, they are revealed to be primary components of the Defense Program identified from the "dark fragments" created by the Defense Program's regeneration due to having their own personalities. It is revealed in Nanoha and Reinforce's Paths of the story that Reinforce herself is a Material of the Defense System which tries to reconstruct her while regenerating the Book of Darkness. In The Gears of Destiny, Material-L, Material-S and Material-D begin regenerating once again, it is revealed that were actually materialized again due to the unsealing (regeneration) of the system Unbreakable Dark. It further reveals that the Materials (aside from possibly Reinforce and her copy: the new Will of the Book of Darkness) once together with the U-D used to make up the Tome of the Purple Sky. Which is where their driving need to find the U-D came from.
None of the Materials nor U-D were aware of their origins (having no memory of their history aside from their time in the Book of Darkness) until Stern analyzed U-D herself and as such whether or not Reinforce (who also doesn't remember her origins) like the other Materials and U-D came from the Tome of the Purple Sky has not been revealed (though before Stern's analysis of U-D it was assumed by Dearche that Reinforce was from an earlier era).
Within the game, the Materials are secret characters who combine the strengths of their bases with those of two others, making them extremely powerful (e.g. Material-S has Vita's skill in melee and Zafira's defense in addition to Nanoha's abilities).