That one's better to understand... or I hope so. XD
Well. okay, this may be a bit complicated, but I'll try to explain it as easy as I can.
Let's say, you want to adopt a little puppy. You go to the adoption page, apply for one and so on. Now, you have to decide if you want to keep your adopted character all to yourself or if you want to let it breed in the next generation.
For example, you adopted the character to write a story - of course you don't want them to have anything to do with charries who will not appear in said story.
But if you'd like to leave your character up for breeding, it will be included in the next generation of breedables. Before it's uploaded, I will make a list with all characters that are up for breeding. You should then choose one of them as a mate for your character (of course you have to ask the owner first :3), then the adoption will be released. This is also a way to find new friends on dA!
The cubs are related to your character now, except if the new owner wants to keep tehm "private", like I explained above. Of course you can refuse your character to be the parent of them if you want, then they will "grow up" as orphans
TL;DR, let's say we have a dog named Rex. Rex gets adopted by a deviant. If they choose to keep Rex "private" and not have any relations to other characters here at BreedingStation, they can do so. Otherwise, Rex can find a mate when he's grown up and breed. Now if the owner of Rex doesn't want him to be related to his mate/litter, that's okay, otherwise you have a cute little family!
Hope that wasn't too hard to understand. XD