taste

1250–1300; (v.) Middle English tasten to touch, taste < Old French taster to touch, explore by touching (Middle French: to touch, taste); cognate with Italian tastare, Provençal, Old Spanish tastar < ?; (noun) Middle English tast sense of touch, a trying, tasting < Old French, derivative of taster

17. Taste, flavor, savor refer to a quality that is perceived when a substance is placed upon the tongue. Taste is the general word: the taste of roast beef. Flavor is a characteristic taste, usually of a pleasing kind, and as of some ingredient put into the food: lemon flavor. Savor, much less common than taste or flavor, implies pleasing scent as well as taste or flavor, and connotes enjoyment in tasting: The sauce has an excellent savor.

The English noun taste (Middle English tast ) is derived from the Middle English verb tasten “to taste (food, medicine), perceive a flavor, palpate or feel (a patient), experience or feel something (also referring to sexual feeling), test someone or something, attempt.”
Tasten was borrowed from Old French taster “to touch, try,” from an unrecorded Vulgar Latin verb tastāre (or taxtāre or taxitāre ), which is most likely an alteration of a frequentative verb formed from tangere “to touch, tap, taste (food), lay hands on, affect (with emotion), seize, defraud.” (A frequentative verb is one that expresses repetition of an action).
Though the meaning “to try or examine by touch; to feel” is now obsolete, the current figurative meaning “to have a slight experience of something” has developed from that literal use. And of course the primary meaning “to try the flavor of something” is merely referring to another one of our five senses that is stimulated by food taken into the mouth.