The Weave is the work of Weaver, firstborn of the Seven Daemons and Demon of Fate. He divided fate itself into seven fragments:
1. Blood 2. Bone 3. Flesh 4. Soul 5. Mind 6. Spirit 7. Shadow
Lineage
Each fragment carries part of fate's authority. Sorcerers who worshipped Weaver passed the Lineage down through the ages — Ananke is one of the last known priestesses.
Sunny's Quest
Vol 10 (Dark Lord's Dreadful Travelogue) follows Sunny gathering the fragments of the Lineage. Each fragment unlocks a portion of weaving power.
Cosmic Importance
The Weave is the fabric of destiny. Possessing it in full potentially means rewriting the world's fate — hence the conflicts surrounding its fragments.