Porcelain has been in use for over 4000 years in China. It is made from special white clay and fired at a temperature of 1280 degrees centigrade. There are a couple different ways in which these items are decorated.
The most common today is molded, decorated, and glazed. Others are molded and enameled then fired again. The third type is under glaze in blue and red.
The Chinese have always been extremely proficient at porcelain work, and have produced numerous pieces that look like coral, glass, stone, and many other materials.
What's it worth? Take a look at this Porcelain Doll price guide: sold listings for a value indication.