late 15c., santren "to muse, be in reverie," of uncertain origin despite many absurd speculations. Meaning "walk with a leisurely gait" is from 1660s, and may be a different word. Klein suggests this sense of the word derives via Anglo-French sauntrer (mid-14c.) from French s'aventurer "to take risks," but OED finds this "unlikely." Also see here. Related: Sauntered; sauntering.