early 14c., brasile, "brasilwood," name of a type of red wood from an East Indian tree, used in making dye (in modern times known as sappan-wood or Indian redwood), from Medieval Latin brasilium, Old French bresil, which probably is related to brese "embers," and like it from a Germanic source (compare braze (v.1)), from PIE root *bhreu- "to boil, bubble, effervesce, burn," and so called for resemblance of color to a glowing ember. But as the product came to Europe via India perhaps this is a folk-etymology of some word in Arabic or another Asian language (an Old Italian form, verzino, suggests to some a possible connection with Arabic wars "saffron").
The same word for the same stuff entered Portuguese and Spanish (brasil) and Italian (brasile). The South American country was named Santa Cruz by its "discoverer," Pedro Alvarez Cabral (1500), but within a decade on maps it began to be called terra de brasil "red-dyewood land" because it produced a valuable red dyewood similar to East Indian type, and that name predominated from 1550s.
Complicating matters is Hy Brasil, a name attested since early 14c. for a legendary island or rock in the North Atlantic off the west coast of Ireland. It is so-called perhaps from the "red dyewood" word by association with Pliny's Insulae Purpurariae ("Purple Islands") in the Atlantic off the coast of Morocco.