This is a grass grown exclusively for grain. It is a member of the wheat family (Triticae) and should not be confused with Rye Grass which is a type of Fescue.
Rye originated in Turkey and was cultivated in the Neolithic around an archaeological site called "Can Hasan III". This cereal crop does not appear again until the Bronze Age on Roman sites. The grain has been cultivated since then throughout Central and Eastern Europe, especially in Western Germany and Eastern France.
When used as a sole ingredient, Rye has a bitter taste. For this reason, it has often been used in a mix of ingredients or used for animal fodder. In cool climates, Rye does well, but it is susceptible to infection by the Ergot fungus which can make the grain toxic which can be a serious problem in warmer climates.