
Toma has pretty much gotten it. They are Important because people's knowledge of you gives you power. The bigger the story, the more power it gives, and once you have a certain amount, it qualifies them as a constellation.
I will use the Christian nebula for example. The story has mentioned several smaller angels who are kinda obscure. This is because they are kinda known but do not truly stand out. On the other hand, a majority of the World knows about Jesus and several of his stories. Since a majority of the World knows of it, it is a large fabel and gives immense power

Constellation's incarnation is someone whose body the constellation who is sponsoring them can use as their vessel. Using incarnation body as a vessel means the constellation doesn't have to be 'present' somewhere themselves but they can still be there through their incarnation. Like for example, if a constellation from Eden has an incarnation on earth, they don't personally have leave Eden to go to earth. They can descent there by using their incarnation's body. And incarnations in turn get power, and ideally, support from their constellation sponsors.

I’ll try to roughly explain it
Sponsors (for now) are just constellations in the sky. The constellations can be anyone, most of them are historical or mythical stories characters tho like uriel sunwukong etc
Incarnation can have two meanings (for now)
1. How the constellations call the people they sponsor
(Ex; if the demon king of salvation is the sponsor of yoo joonghyuk, he will call yoo joonghyuk his incarnation)
2. The physical form constellations takes after, which usually are humans or the humans they sponsor
Ex: Asmodeus incarnation right now is a little girl, that is not how he looks like, its just the form he takes after to appear as in the complex

Think of it as a company system
Constellation - Boss/Executives
Incarnation - Employees
Story - Your life/salary/work/status
Fable - Achievements/Award/Promotion (Like Employee of the Year or increase in salary)
Having a strong Constellation in a company will help you strive and have a high promotion status. If your work isn't interesting and you never try your best to improve, you will never get promoted or will forever stay low.
I hope this helps.
I dont understand about the fables anymore. What are they and what are they used for. Sponsors and incarnations too yet i keep reqding it UnU