c. 1500, santren "to muse, be in reverie," a word of uncertain origin. The meaning "walk with a leisurely gait" is from 1660s, and may be a different word which, despite many absurd speculations, also is of unknown origin. Klein prints the theory (held by Skeat and Murray) that this sense of the word derives via Anglo-French sauntrer (mid-14c.) from French s'aventurer "to take risks." Century Dictionary finds the theory involves difficulties but "it is the only one that has any plausibility," but OED finds it "unlikely." Also see here. Related: Sauntered; saunterer; sauntering.
"a leisurely stroll, a ramble," 1828, from saunter (v.). Earlier it meant "idle occupation, diversion" (1728); "leisurely, careless way of walking" (1712).