Semolina is the coarse, purified wheat middlings

Wheat middlings

Wheat middlings or wheat mill run, stated by AAFCO, is coarse and fine particles of wheat bran and fine particles of wheat shorts, wheat germ, wheat flour and offal from the "tail of the mill"....

 of durum

Durum

Durum wheat or macaroni wheat is the only tetraploid species of wheat of commercial importance that is widely cultivated today...

 wheat

Wheat

Wheat is a cereal grain, originally from the Levant region of the Near East, but now cultivated worldwide. In 2007 world production of wheat was 607 million tons, making it the third most-produced cereal after maize and rice...

 used in making pasta

Pasta

Pasta is a staple food of traditional Italian cuisine, now of worldwide renown. It takes the form of unleavened dough, made in Italy, mostly of durum wheat , water and sometimes eggs. Pasta comes in a variety of different shapes that serve for both decoration and to act as a carrier for the...

, and also used for breakfast cereal

Breakfast cereal

A breakfast cereal is a food made from processed grains that is often, but not always, eaten with the first meal of the day. It is often eaten cold, usually mixed with milk , water, or yogurt, and sometimes fruit but sometimes eaten dry. Some cereals, such as oatmeal, may be served hot as porridge...

s and pudding

Pudding

Pudding most often refers to a dessert, but it can also be a savory dish.In the United States, pudding characteristically denotes a sweet milk-based dessert similar in consistency to egg-based custards, though it may also refer to other types such as bread and rice pudding.In the United Kingdom and...

s. Semolina is also used to designate coarse middlings from other varieties of wheat, and from other grains such as rice and corn.
The term semolina derives from the Italian word "semola" that derives from the ancient Latin simila, meaning "flour

Flour

Flour is a powder which is made by grinding cereal grains, other seeds or roots . It is the main ingredient of bread, which is a staple food for many cultures, making the availability of adequate supplies of flour a major economic and political issue at various times throughout history...

," itself a borrowing from Greek σεμῖδαλις (semidalis), "groats".