From Destinypedia, the Destiny wiki
The Anthem Anatheme is a paracausal ability described in several pieces of lore within the Destiny universe. It is defined as the desire to change one's reality to suit one's purposes, or "to dominate the objective universe with the subjective will".
According to the Darkness itself, in the primordial state before time or the universe began, entities existed which derived sustenance from the gradient between "what was and what might be." This appears to allude to the Anthem Anatheme, and possibly hints at the origins of beings such as the Ahamkara and Worms, which continue to sustain their existence using the differences between possible and actual realities.
Several paracausal beings utilize, invoke or draw power from the Anthem Anatheme in some way; the most notable examples are the Ahamkara and the Worm Gods, which are theorized by Medusa to have evolved separately in competition for the same ecological niche. Ahamkara feed off of the wishes (which are manifestations of the Anthem Anatheme) of other beings to grow in size, whereas the Worm God Xol transformed himself into a weapon after his physical death in order to fulfill the Anthem Anatheme for the wielder.
Beings who draw power from the Anthem Anatheme are known to use a specific phrase, "O/Oh (subject) mine," when addressing other beings. This is theorized by Medusa to invoke an ontomorphic effect, placing the target in a cage of "o" (activational, specific, appealing, and naming) and "mine" (defining ownership and subordination).  Even the Cabal Emperor Calus invokes the Anthem Anatheme by addressing his favorite Guardian as "O champion mine".
The Awoken as a whole are not subject to the Anthem Anatheme, as their desires are aligned almost perfectly with those of their Queen, and the Queen herself has very little desire to change reality for her own purposes. It was this alignment which allowed the Ahamkara Riven to coexist with the Awoken in relative peace for so long, although Uldren Sov was prohibited from interacting with Riven because his desires for himself were less attuned to his reality.