c. 1400, "faculty of perception," also "meaning, import, interpretation" (especially of Holy Scripture), from Old French sens "one of the five senses; meaning; wit, understanding" (12c.) and directly from Latin sensus "perception, feeling, undertaking, meaning," from sentire "perceive, feel, know," probably a figurative use of a literally meaning "to find one's way," or "to go mentally," from PIE root *sent- "to go" (source also of Old High German sinnan "to go, travel, strive after, have in mind, perceive," German Sinn "sense, mind," Old English sið "way, journey," Old Irish set, Welsh hynt "way"). Application to any one of the external or outward senses (touch, sight, hearing, etc.) in English first recorded 1520s.
A certain negro tribe has a special word for "see;" but only one general word for "hear," "touch," "smell," and "taste." It matters little through which sense I realize that in the dark I have blundered into a pig-sty. In French "sentir" means to smell, to touch, and to feel, all together. [Erich M. von Hornbostel, "Die Einheit der Sinne" ("The Unity of the Senses"), 1927]
Meaning "that which is wise" is from c. 1600. Meaning "capacity for perception and appreciation" is from c. 1600 (as in sense of humor, attested by 1783, sense of shame, 1640s).