Century Eggs are a chinese delicacy. Although they do look weird compared to a normal egg, they actually taste great. A great way to prepare it is to peel the shell, apply a small amount of chinese black vinegar and sugar, then slice it up and mix it. It tastes great with just plain rice and can also be comboed with other ingredients for additional flavors.
Although they are called Century Eggs, they take at most a few months to prepare (or you could just buy them at any chinese supermarket). The traditional method to make century eggs was by preserving chicken or duck eggs in a mixture of salt, lime, and ash, then wrapping in the whole package in rice husks and leaving them for several weeks.
After the preservation period, the yolk becomes a dark green / grayish mass and the egg white becomes a dark brown, transparent solid.
The direct translation of the Chinese term for the Century Egg would be pine flower egg.
Just as a side note, I've eaten them, they taste great, and I'm still alive. No negative side effects have been noted so far. I personally actually really like Century Eggs.