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.