The Singers are a yet unknown group whom the Chandrian have reason to fear.
Kvothe mentions in Ch. 38 of The Wise Man's Fear a nomadic group called The Tahl who use their voices instead of having warriors. They are also said to have the ability to heal the sick and make trees dance.
The singers are likely powerful namers. In the story Kvothe hears from Skarpi in Tarbean, Aleph empowers several Ruach with white fire. "The fire flickered in their eyes and they saw into the deepest hearts of men. The fire filled their mouths and they sang songs of power." This is not the only case of singing being involved in powerful naming. During Kvothe's fight with Felurian, his "mind was filled with the sudden song of her. [He] drew a breath and sang it out in four hard notes." Elodin later tells Kvothe that he was naming Felurian which was impossibly difficult.
"Then the fire settled on their foreheads like silver stars..." -Skarpi (continued)
"I saw myself reflected in her eyes, naked among the cushions. My power rode like a white star on my brow." -Kvothe during the fight with Felurian