The gods cannot walk on the main material plane of the Kain Continent; they are all repelled to their respective divine realms. However, to compete for faith and increase their divine power, finding ways to descend to the main material plane is necessary.
Divinity serves as such a medium.
Just like the bishop in the cathedral, who had a trace of divinity gathered from his fervent faith, it was because of this trace of divinity that Balda the Flame Dragon could descend upon his body.
Sylvie had also heard the term "vessel" from Anna. Perhaps it could be understood this way: the awakened demi-humans are excellent vessels.
