What does it mean  when a pet is descendant of heroes? Also when you breed pets who are both descendant o heroes why is there child not also descendant? 

It's also called Genetic Power. Basically if you train two beasts to level 50 (maximum) and then breed them, the offspring gains 1 GP point, which gives +10 bonus to all stats.

GP can go up to 3 stages, so GP3 beasts are generally strongest and more desirable.

If your beast has 0, 1 or 2 GP you must raise them to level 50 in order to pass on their GP, or add more. If both parent-beasts already have 3 then I think you can breed them at any time and all offspring will have 3.

I guess the idea behind it is "quality over quantity", encouraging us to train up our beasts to reach their full potential instead of breeding early and all over the place. Like in the real world, if you breed dogs or horses or other animals, you wait for them to mature and succeed at work/shows, to prove their ability before you decide to breed further.

Thank you for the help!

No problem :) On the battle arena, it's also called Heritage (and represented by green stars) and on the profile page of a beast with GP, if you hover over a stat it will say something like "Pedigree bonus: +30"

Pedigree is the best word for it, I think. Descendant of Heroes is just a cooler-sounding name.