Pierogi are dumpling

Dumpling

Dumplings are cooked balls of dough. They are based on flour, potatoes or bread, and may include meat, fish, vegetables, or sweets. They may be cooked by boiling, steaming, simmering, frying, or baking. They may have a filling, or there may be other ingredients mixed into the dough. Dumplings may...

s of unleavened dough

Dough

Dough is a paste made out of any cereals or leguminous crops by mixing flour with a small amount of water and/or other liquid. This process is a precursor to making a wide variety of foodstuffs, particularly breads and bread-based items , flatbreads, noodles, pastry, and similar items)...

 - first boiled, then they are baked or fried usually in butter with onions - traditionally stuffed with potato filling, sauerkraut

Sauerkraut

Sauerkraut , directly translated from German: "sour cabbage", is finely shredded cabbage that has been fermented by various lactic acid bacteria, including Leuconostoc, Lactobacillus, and Pediococcus. It has a long shelf-life and a distinctive sour flavor, both of which result from the lactic acid...

, ground meat, cheese, or fruit. Of central and eastern European provenance, they are usually semicircular, but are rectangular or triangular in some cuisines.

The Polish word pierogi is plural; the singular form pieróg is rarely used, as a typical serving consists of several pierogi.
The origins of pierogi come from Poland.