I think you have to loose to a goblin female but not sure, I remember seeing this while playing earlier versions but did not care much about it to notice now. Possibly it could've been taken out entirely, if you ask me goblins laying eggs sound kind of meh.

Yea it requires you being defeated by a Goblin (Female) and then failing 4 endurance checks. Once she lays her eggs you'll need to be a bottom to one of the 3. Centaur/Harpy/Werewolf. Then wander around awhile and you'll get an "Encounter" screen, which will be the birth. I'd recommended just saving after the eggs then finding one of the three  and then reloading after each birth just to expedite the process.