Depending on configuration settings, when a monster has a child the genetics are based on both parents of each monster or just the parents of the child. The 'parent trait' then shows you what parents the monster had that led to its creation (i.e. you may see that one parent shares a similar skin color, combination of breast size, etc.)
You can edit the configuration file to change it so that children born either pull up to grandparents genetically (leading to a wider diversity of outcomes), or from just its own parents. I will say that even if you try to limit it to just parents, some traits just do not pass on easily, such as unusual skin colors like albino/melanin.
As for what pregnancy does... "when a mommy monster and the protagonist have a lot of sex in a slave dungeon, mommy gets really big and a child is born! That child then goes on to become an adult instantly and is added to the slave dungeon to either be sold for profit or be broken in by her father"
*two random things as well:
1. When you start up the game you create your own character and if you impregnate a monster with these genetics then the child will have a human parent (you) so any traits you have may be passed on. For example, if you made your hair green and did it with a brown harpy, the child may have green feathers. Once you do stuff with a tamed slave, that slave will overwrite your genetics if you want, meaning that any monster you do afterwards will have the first monster as the genetic parent.
For example, if you did a harpy and a lamia when they were both chained up then their children would be a human/harpy and a human/lamia. If however you tamed the harpy, did her and got her genetics, then had sex with the lamia, then the lamia's child would be a harpy/lamia. All this is to say that if you want to change what genetics you are passing on, it's an option in the dungeon and would recommend if you care about trying to make a "perfect waifu" or whatever. I will also bring up how children born from differing races are counted as "mixed", so even if you did create a child that resembles another race somehow that child would not count as the race it looks like (this mostly matters if you are selling them, mixed children have various factors determining their cost so a mixed harpy/lamia sells for little while a mixed alien/dragon would likely sell for more). I'm pretty sure this also means that anything mixed with slime would not replicate when tamed, but I am unsure.
2. Incest is a game variable... sorta. Each monster has a 'magic' stat, and the higher it is the more likely their children will have some kind of oddity, including an unusual amount of eyes or limbs. Breeding the same genetics over time (such as getting a monster pregnant, then getting their genes and getting the daughter pregnant with those genes) will cause the magic stat to raise overtime. I won't judge, and it's a possibility no matter what (some monsters you find will have a high base stat anyway), just letting you know.
