(1) The primary meaning of the word is "taste," "flavor" (from Latin sapor, "taste"). So in Mt 5:13; Lu 14:34, "if the salt have lost its savor" (moranthe, "become tasteless," "insipid," so as to lose its characteristic preserving virtue).
(2) But generally it has the meaning of "smell," "odor":
(a) once of evil odor: "Its stench shall come up, and its ill savor shall come up" (Joe 2:20);
(b) elsewhere in the sense of pleasant smell. In the Old Testament, with the exception of Ex 5:21 and the King James Version So 1:3 (the Revised Version (British and American) "fragrance"), it is always accompanied by the adjective "sweet." It stands for the smell of sacrifices and oblations, in agreement with the ancient anthropomorphic idea that God smells and is pleased with the fragrance of sacrifices (e.g. "Yahweh smelled the sweet savor," Ge 8:21; "to make a sweet savor unto Yahweh," Nu 15:3; and frequently).
In the New Testament, "savor" in the sense of smell is used metaphorically:
(a) once the metaphor is borrowed from the incense which attends the victor’s triumphal procession; God is said to make manifest through His apostles "the savor of his knowledge in every place" as He "leadeth" them "in triumph in Christ" (2Co 2:14; see Triumph.
(b) Elsewhere the metaphor is borrowed from the fragrant smell of the sacrifices. The apostles "are a sweet savor of Christ unto God" (2Co 2:15), i.e. they are, as it were, a sweet odor for God to smell, an odor which is pleasing to God, even though its effect upon men varies (to some it is a "savor from death unto death," i.e. such as is emitted by death and itself causes death; to others it is "a savor from life unto life," 2Co 2:16). By the same sacrificial metaphor, Christ’s offering of Himself to God is said to be "for a sweet smelling savor" (Eph 5:2 the King James Version, the Revised Version (British and American) "for an odor of a sweet smell"; the same phrase is used in Php 4:18 of acts of kindness to Paul, which were "a sacrifice acceptable, well-pleasing to God").
(3) Once it is used in the figurative sense of reputation: "Ye have made our savor to be abhorred (literally, "our smell to stink") in the eyes of Pharaoh" (Ex 5:21). Compare the English phrase, "to be in bad odor."
The verb "to savor" means:
(1) intransitively, to taste or smell of, to partake of the quality of something, as in the Preface of the King James Version, "to savour more of curiosity than wisdome," or
D. Miall Edwards