"yellow malleable alloy metal, harder than copper," Old English bræs "brass, bronze," originally any alloy of copper, in England usually with tin (this is now called bronze), later and in modern use an alloy of roughly two parts copper to one part zinc. A mystery word, with no known cognates beyond English. Perhaps akin to French brasser "to brew," because it is an alloy. It also has been compared to Old Swedish brasa "fire," but no sure connection can be made. Yet another theory connects it with Latin ferrum "iron," itself of obscure origin.
Words for "brass" in other languages (such as German Messing, Old English mæsling, French laiton, Italian ottone) also tend to be difficult to explain. As brass was unknown in early antiquity (it was well-known to Strabo, 1c., but not mentioned by Homer), the use of the English word in Bible translations, etc., likely means "bronze." The Romans were the first to deliberately make it.
When works of Greek and Roman antiquity in 'brass' began to be critically examined, and their material discriminated, the Italian word for 'brass' (bronzo, bronze) came into use to distinguish this 'ancient brass' from the current alloy. [OED]
Rhetorically or figuratively it was the common type of hardness, durability, or obduracy since late 14c. The meaning "effrontery, impudence, excessive assurance" is from 1620s. Slang sense of "high officials" is first recorded 1899, from their insignia. Meaning "brass musical instruments of a band" is from 1832.