Cutting a long story short, century eggs are preserved quail, duck, or chicken eggs. They have a bunch of names, by the way, such as millennium eggs, thousand-year eggs, or khai yiao ma which in Thai means 'horse urine eggs.' Why? Due to their acid smell, there is the misconception that these eggs are made by soaking them in horse urine.
Legend has it that they were discovered accidentally; these eggs have existed for centuries during the Ming Dynasty in China. An inhabitant of Hunan decided to try duck eggs which were found in slack lime.
By the way, modern eggs are not preserved for a century, one thousand years, or a millennium. Absolutely not. A period from a few weeks to a few months will be enough for them to soak in a saline solution, a mixture of wood lime, salt, ash, and clay or tea with rice straw. The pH of the egg rises to 9-12 and breaks down some of the egg's fats and proteins into flavorful molecules. Under such conditions, the yolk turns into a cheese-like, creamy substance, and the white transforms into a dark jelly. The surface of that jelly may be covered with adorable pine-tree patterns or crystalline frost. In theory, the white doesn't have much flavour by contrast with the yolk which has a strong smell of sulfur and ammonia and is rumoured to have a complex earthy aroma.
Century eggs are often served with pickled ginger root and can accompany rice porridge or congee as well as they can be eaten alone.