The Chinese call these Guotie, the Japanese call them Gyoza, and in the US, we tend to call them potstickers. When I am eating them, I am not so particular about what they are called; I am focused on how much I enjoy eating them.
If you have never had them, they are made with a circular skin and are then filled with a mixture of some sort, typically ground meat, and or vegetables. They are then sealed by pressing the edges together or by crimping them. They are usually served with a soy/vinegar dipping sauce. They are one of those things that are amazing to eat and seem complex to prepare but they are not. Usually when I make them, I make several dozen at a time, as they do not last long in our house. My favorite recipes for making gyoza are at http://www.food.com/recipe/japanese-gyoza-41660 and for guitoe (Chinese pot stickers) at http://www.food.com/recipe/chinese-pot-stickers-13320. While both recipes are time consuming, they are better then the guitoe you will find at most Chinese restaurants.