Could someone explain what Descendant of Heroes is? I see it on the quests but haven't a clue what it is or how to get 1.

Descendant of Heroes is the same thing as Genetic Power.

From the FAQ:

Genetic Power is a bonus which child will get if the parents were properly trained before conceiving a baby.

Genetic Power gives +10 bonus to each characteristic for each Grade (in total +60 characteristics bonus for each Grade). The other profit from Genetic Power are access to temples which give you items for free if you qualify for their Genetic Power requirements, and the ability to fulfill the most high-paid quests.

The rules of acquiring Genetic Power:

1. If both of the parents have level 50, their child will get +1 Genetic Power.
   If one of the parents is level 50 and the other is not, the child will get +1 Genetic Power if it has 7 or more dominant genes from the level 50 parent.
2. If both of the parents has similar grade of Genetic Power, the child will get this grade and +1 grade if one or both parents have maximum level (according to the first rule)
3. If parents have a difference of 1 grade of Genetic Power, the child will get the higher grade if it has inherited 7 or more dominant genes from the parent with higher grade.
4. If parents has a difference of 2 or more grades of Genetic Power, the child won't get Genetic Power grade for parents' genes, it can get only 1 Grade for parents' levels.

Some examples to illustrate these rules:

1. Lvl 50 pet GP grade 2 x Lvl 50 pet = Child GP Grade 1
2. Lvl 50 pet GP grade 1 x Lvl 50 pet = Child GP Grade 2 (if there are 7 or more dominant genes from parent with Grade 1) or Grade 1 (if there are less than 7 dominant genes from parent with Grade 1)
3. CLvl 50 pet GP Grade 2 x Lvl 50 pet GP Grade 1 = Child GP Grade 3 (if there are 7 or more dominant genes from parent with Grade 2) or Grade 2 (if there are less than 7 dominant genes from parent with Grade 2)