1520s, of animals, "make a quick bite" (intransitive), from or cognate with Dutch or Low German snappen "to snap," which could be related to Middle Low German or Middle Dutch snavel "bill, beak," which Watkins traces to a hypothetical Germanic root *snu- forming words having to do with the nose, imitative of a sudden drawing of breath (see snout). Ultimately imitative. Compare earlier gnappen "snap with the teeth" (c. 1300).
The intransitive meaning "break suddenly or sharply" is from c. 1600. The transitive sense of "take or catch unexpectedly with a bite" is from 1560s; that of "shut with a sharp sound" is from 1570s.
The meaning "come or move into place with a snap" is attested from 1793. In a broader sense of "do (something) hastily or eagerly" it is attested by 1798. The meaning "take an instant photograph" is from 1890. The U.S. football sense is by 1887 (see the noun).
To snap at "speak sharply or harshly to" is from 1570s. To snap in the mental sense of "suddenly lose control, composure, or sanity" is from 1970s. Related: Snapped; snapping.
In reference to the noise made with the fingers and palm, from 1670s (snap with one's fingers). The phrase snap out of it "change one's behavior suddenly" is recorded by 1907. The snapping turtle, large, ferocious freshwater turtle of the U.S., is so called by 1784, for its powerful bite. Snap-brim (adj.) in reference to a type of hat is from 1928.