Old English crisp "curly, crimped, wavy" (of hair, wool, etc.) from Latin crispus "curled, wrinkled, having curly hair," from PIE root *sker- (2) "to turn, bend."
It began to mean "brittle" 1520s, for obscure reasons, perhaps based on what happens to flat things when they are cooked. Sense of "neat, brisk, having a fresh appearance" (1814) is perhaps a figurative use, or perhaps a separate word. Of air, "chill, bracing" by 1869.
As a noun from mid-14c., originally the name of a light, crinkly material formerly used for kerchiefs, veils, etc.; late 14c. as a kind of pastry. By 1826 as "overdone piece of anything cooked" (as in burned to a crisp). Potato crisps (now the British version of U.S. potato chips, but not originally exclusively British) is by 1897; as simply crisps by 1935. In U.S., crisps began to be used by 1903 in trade names of breakfast cereals. Related: Crisply; crispness.
late 14c., "to curl, to twist into short, stiff waves or ringlets" (of the hair, beard, mane, etc.) from crisp (adj.) or else from Old French crespir, Latin crispare, from the adjectives. Meaning "to become brittle" is from 1805. Related: Crisped; crisping; crispation.