The idea of paths came from noticing that the Nine Titans are sent to a random baby among the Subjects of Ymir, regardless of distance or blood relations, if they die without being eaten. This implies that the Subjects of Ymir are all connected by something invisible, and what connects them are called paths.
In the year 990 B1, the soul of Ymir Fritz came to inhabit the unknown land where the paths manifested after her death, under the form of her younger self when she first attained the Power of the Titans thirteen years prior. At this point, the Coordinate was newly formed, only having three paths manifesting from it, likely representing Ymir's daughters: Maria, Rose and Sina Fritz.
As Zeke Jaeger is dying from the wounds inflicted by a Thunder Spear explosion, he has a vision of Ymir Fritz, in tattered clothes, in a world full of sand. A Titan approaches him and opens its abdomen to put his body inside. Zeke awakens inside the unknown land to Ymir rebuilding his body using the surrounding earth, and he sees trails of light in the sky above. Zeke later comes out of the Titan, fully recovered, and speculates that what he just saw are paths.
Overview: The idea of paths came from noticing that the Nine Titans are sent to a random baby among the Subjects of Ymir, regardless of distance or blood relations, if they die without being eaten. This implies that the Subjects of Ymir are all connected by something invisible, and what connects them are called paths. Paths serve as channels for the transportation of several things, such as, but not limited to, memories and thoughts from other Subjects of Ymir, and the flesh and bones that make up a Titan's body.
History: In the year 990 B1, the soul of Ymir Fritz came to inhabit the unknown land where the paths manifested after her death, under the form of her younger self when she first attained the Power of the Titans thirteen years prior. At this point, the Coordinate was newly formed, only having three paths manifesting from it, likely representing Ymir's daughters: Maria, Rose and Sina Fritz. As Ymir's daughters began to birth children of their own, new paths began to manifest from the Coordinate, in which Ymir's power was eventually separated into the Nine Titans.
Story: As Zeke Jaeger is dying from the wounds inflicted by a Thunder Spear explosion, he has a vision of Ymir Fritz, in tattered clothes, in a world full of sand. A Titan approaches him and opens its abdomen to put his body inside. Zeke awakens inside the unknown land to Ymir rebuilding his body using the surrounding earth, and he sees trails of light in the sky above.
Source: Path (Anime), available under CC BY-SA 3.0.