Baby duck eggs, as sold by Asian markets, aren't laid by baby ducks - they contain them. Thanks to Fear Factor and other horseshit reality shows, most people have heard of balut or embryonic eggs, but "fertilized egg" should be thought of as a genre of food, not a specific food item.
I always hated those shows in the first place, but especially that aspect of those shows: ohgrossethnicfood. Cheese is pretty fucking disgusting if you didn't grow up in a culture that takes it for granted, and the idea of drinking milk from an animal ought to weird you out a little. I've never liked "oh God look at the things the rubes and brown people eat" television/web sites/etc, and I don't think adults have any business using words like "scary" or "gross" for real food that real people eat. That doesn't mean everyone is obligated to like or even try everything - but understand that food is food, that there is a reason other people like and eat it, that your lack of appreciation doesn't reflect some actual real-world standard of good and bad.
I'm not crazy about eggplant, century eggs, sweet deviled eggs, flying fish eggs, or fertilized eggs that have developed past a certain point - but I'm not enough of an asshole to think that's a statement about the world instead of a statement about me, you know?
It takes a little over three weeks for a fertilized egg to develop and hatch, and there's a wide variety of possibilities beneath the shell in those three weeks. Most people have probably had an egg with a red spot in the yolk - there's your day one.
When they're let to develop more than that, though, developed deliberately and sold as food products, they're boiled and served warm to eat, sometimes seasoned with hot sauce, soy sauce, etc.
Fertilized eggs are a snack throughout Southeast Asia, with the cook date varying from place to place, ethnicity to ethnicity.
Personally, my fertilized egg preference is, if I remember right, around the two-week mark - still almost entirely a hard-boiled egg, but with a richer yolk, a small piece of meat that isn't yet recognizably anything, and a flavor like the whole thing has been cooked in light duck broth (... which it has).
... this egg is a bit more advanced than that, but short of the 21 day mark when the egg contains mostly developing baby duck, with bones you need to crunch through when you eat it.
In the first photo, you can see the yolk material at the top of the opened egg, and the developing duck about the size of a silver dollar (duck eggs are about, what, half again as big as a "jumbo" chicken egg) curled up beneath that.
Taking the shell off gives you another view: we've still got the duck, with the yolk directly above it, and the rest is egg white, most of which is hard and inedible.
Clockwise from nine o'clock: the little duck again; the mostly inedible white; the yolk.
The yolk is actually very good, but this isn't the stage of fertilized egg I'd seek out - the embryo is just a little too developed for me at this point. That said, there isn't a strong flavor - with your eyes closed, there's nothing strange going on here.