Basically, after working your way (around 4h of gameplay in a cookie clicker game) you get enough love points with the character, you have developed their relations. You can have sex, which can lead to pregnancy. Pregnancy, is a few in game day long, with one stage growing belly that activate as soon as you leave the character. Classic.
Then after a while you get a baby, which you can use a special potion (you don't get a yes no option it just does it when you click on the baby while having the item) which makes it an adult with no face.
You can also have a daughter, but her mother is broken in my game so I don't know how I got here in the first place, and since fucking your children isn't for me, I don't interact with her...
Oh and pregnancy it itself is random (mini game) with a threshold that you have to reach, which varies based on the day