Middle English Grek, from Old English Grecas, Crecas (plural) "Greeks, inhabitants of Greece," an early Germanic borrowing from Latin Graeci "the Hellenes," apparently from Greek Graikoi. The first use of Graikhos as equivalent to Hellenes is found in Aristotle ("Meteorologica" I.xiv).
A modern theory (put forth by German classical historian Georg Busolt, 1850-1920), derives it from Graikhos "inhabitant of Graia" (literally "gray," also "old, withered"), a town on the coast of Boeotia, which was the name given by the Romans to all Greeks, originally to the Greek colonists from Graia who helped found Cumae (9c. B.C.E.), the important city in southern Italy where the Latins first encountered Greeks. Under this theory, it was reborrowed in this general sense by the Greeks.
The Germanic languages originally borrowed the word with an initial "-k-" sound (compare Old High German Chrech, Gothic Kreks), which probably was their word-initial sound closest to the Latin "-g-" at the time; the word later was refashioned.
It is attested from late 14c. as "the Greek language." The meaning "unintelligible speech, gibberish, any language of which one is ignorant" is from c. 1600. The meaning "member of a Greek-letter fraternity" is student slang, 1884.
It was subtle of God to learn Greek when he wished to become an author — and not to learn it better. [Nietzsche, "Beyond Good and Evil," 1886]