Baker's Evangelical Dictionary of Biblical Theology 
Finding favor means gaining approval, acceptance, or special benefits or blessings. There is also a close association among favor, grace, and mercy, which are sometimes used to translate the same Hebrew and Greek words (such as hen [ Genesis 6:8; Exodus 33:12-13 ), receive favor and honor from the Lord ( Psalm 84:11 ). In Moses' blessing on the twelve tribes he speaks of Joseph's prosperity and fruitfulness as the one who enjoyed God's favor ( Deuteronomy 33:16 ). Gabriel told Mary ( Luke 1:30 ) that she had "found favor with God" and would bear the Christ-child. When Christ was born the angelic host announced to the shepherds that God would send "peace to men on whom his favor rests" ( Luke 2:14 ). At age twelve Jesus enjoyed the favor of God and men as he "grew in wisdom and stature" ( Luke 2:52 ), a description similar to the one about the boy Samuel ( 1 Samuel 2:26 ).
Often the bestowal of God's favor comes in answer to prayer as people cry out for mercy. Moses pleaded that God would spare Israel in spite of their sinful worship of the golden calf ( Exodus 32:11 ). Moses prayed that he might know God and learn his ways so that his favor might continue ( Exodus 33:12-13 ). Sinful kings such as Manasseh humbled themselves and sought the Lord in their distress, and he graciously showed them favor ( 2 Kings 13:4; 2 Chronicles 33:12 ). Sometimes, however, the Lord withheld his compassion and brought judgment on his people (cf. Isaiah 27:11 ).
Still, when the full force of his judgment struck Israel, God did not abandon the nation but restored them from exile. He showed compassion to this people and saved them from their distress ( Psalm 106:4; Isaiah 60:10 ). Isaiah calls this deliverance the "time" or "the year of the Lord's favor" (49:8; 61:2), which is linked with the day of salvation in the New Testament ( Luke 4:19; 2 Corinthians 6:2 ). Those who believe the gospel receive the ultimate gift of God's favor: eternal life through Christ.
Human approval can be gained through faithful and effective service. Joseph enjoyed the favor of Potiphar as he wisely administered Potiphar's estate, though ultimately this recognition came through God's blessing ( Genesis 39:4,21 ). Ruth found favor in the eyes of the wealthy Boaz because of her kindness to her mother-in-law, Naomi ( Ruth 2:2,10,13 ). Although David was badly out of favor with Saul, even the Philistines realized how quickly David could have regained that favor through his military skill ( 1 Samuel 29:4 ). A king's favor brought many benefits to the recipient ( Proverbs 16:15 ).
Because of sin God requires sacrifices to make atonement and restore his favor. In the Old Testament animal sacrifices were presented at the sanctuary with the hope that God would accept them and forgive the sins of the offerer ( Leviticus 1:3-4 ). Such acceptance was not automatic, however, for the offerer had to have an attitude of repentance and humility (cf. Genesis 4:4-5; Micah 6:7-8 ). When Christ died on Calvary, the perfect sacrifice was presented, making it possible for all who believe to enjoy God's favor ( 2 Corinthians 6:2 ).
See also Grace
Bibliography . G. Schrenk, TDNT, 2:743-51; W. Zimmerli and H. Conzelmann, TDNT, 9:376-81,392-401.
Vine's Expository Dictionary of OT Words 
Râtsôn ( רָצֹן , Strong'S #7522), “favor; goodwill; acceptance; will; desire; pleasure.” The 56 occurrences of this word are scattered throughout Old Testament literature.
Râtsôn represents a concrete reaction of the superior to an inferior. When used of God, râtsôn may represent that which is shown in His blessings: “And for the precious things of the earth and fullness thereof, and for the good will —of him that dwelt in the bush” (Deut. 33:16). Thus Isaiah speaks of the day, year, or time of divine “favor”-in other words, the day of the Lord when all the blessings of the covenant shall be heaped upon God’s people (Isa. 49:8; 58:5; 61:2). In wisdom literature, this word is used in the sense of “what men can bestow”: “He that diligently seeketh good procureth favor: but he that seeketh mischief, it shall come unto him” (Prov. 11:27). In Prov. 14:35, râtsôn refers to what a king can or will do for someone he likes. This word represents the position one enjoys before a superior who is favorably disposed toward him. This nuance is used only of God and frequently in a cultic context: “… And it [the plate engraved with “holy to the Lord”] shall be always upon his [the high priest’s] forehead, that they may be accepted before the Lord” (Exod. 28:38). Being “accepted” means that God subjectively feels well disposed toward the petitioner.
Râtsôn also signifies a voluntary or arbitrary decision. Ezra told the people of Israel to do the “will” of God, to repent and observe the law of Moses (Ezra 10:11). This law was dictated by God’s own nature; His nature led Him to be concerned for the physical well-being of His people. Ultimately, His laws were highly personal; they were simply what God wanted His people to be and do. Thus the psalmist confessed his delight in doing God’s “will,” or His law (Ps. 40:8). When a man does according to his own “will,” he does “what he desires”: “I saw the ram pushing westward, and northward, and southward; so that no beasts might stand before him, neither was there any that could deliver out of his hand; but he did according to his willand became great” (Dan. 8:4). In Ps. 145:16, the word râtsôn means “one’s desire” or “what one wants” (cf. Esth. 1:8). This emphasis is found in Gen. 49:6 (the first occurrence): “… And in their self-will they [brought disaster upon themselves].”
Râtsâh ( רָצָה , Strong'S #7521), “to be pleased with or favorable to, be delighted with, be pleased to make friends with; be graciously received; make oneself favored.” This verb, which occurs 50 times in the Old Testament, has cognates in Ugaritic, Aramaic, Syriac, and Arabic. Gen. 33:10 contains one appearance of this word: “… thou wast pleased with me.”
Webster's Dictionary 
(1): ( n.) A gift or represent; something bestowed as an evidence of good will; a token of love; a knot of ribbons; something worn as a token of affection; as, a marriage favor is a bunch or knot of white ribbons or white flowers worn at a wedding.
(2): ( n.) Kind regard; propitious aspect; countenance; friendly disposition; kindness; good will.
(3): ( n.) The act of countenancing, or the condition of being countenanced, or regarded propitiously; support; promotion; befriending.
(4): ( n.) A kind act or office; kindness done or granted; benevolence shown by word or deed; an act of grace or good will, as distinct from justice or remuneration.
(5): ( n.) Mildness or mitigation of punishment; lenity.
(6): ( n.) The object of regard; person or thing favored.
(7): ( n.) To resemble in features; to have the aspect or looks of; as, the child favors his father.
(8): ( n.) Appearance; look; countenance; face.
(9): ( n.) Partiality; bias.
(10): ( n.) A letter or epistle; - so called in civility or compliment; as, your favor of yesterday is received.
(11): ( n.) Love locks.
(12): ( n.) To regard with kindness; to support; to aid, or to have the disposition to aid, or to wish success to; to be propitious to; to countenance; to treat with consideration or tenderness; to show partiality or unfair bias towards.
(13): ( n.) To afford advantages for success to; to facilitate; as, a weak place favored the entrance of the enemy.
International Standard Bible Encyclopedia 
fā´vẽr ( חן , ḥēn , רצון , rācōn , with other Hebrew words; χάρις , cháris ): Means generally good will, acceptance, and the benefits flowing from these; in older usage it meant also the countenance, hence, appearance. Alternating in English Versions of the Bible with "grace," it is used chiefly of man, but sometimes also of God ( Genesis 18:3; Genesis 30:27; Genesis 39:21; Exodus 3:21; 2 Samuel 15:25 , "in the eyes of Yahweh," etc.). It is used perhaps in the sense of "countenance" in Proverbs 31:30 , "Favor is deceitful, and beauty is vain" (the King James Version), where for "favor" the Revised Version (British and American) has "grace"; the reference is to external appearance. "Favored" is used in the sense of "appearance" in the phrase "well-favored" ( Genesis 29:17; Genesis 39:6; Genesis 41:2 , Genesis 41:4 ).; conversely, "ill-favored" ( Genesis 41:3 , Genesis 41:4 ). For "favor" the Revised Version (British and American) has "have pity on" ( Psalm 109:12 ), "good will" ( Proverbs 14:9 ), "peace" ( Song of Solomon 8:10 ); the English Revised Version "grace" (Rth 2:13), the American Standard Revised Version "kindness" ( Esther 2:17; Daniel 1:9 ), etc. In the American Standard Revised Version "the acceptable year of the Lord" ( Isaiah 61:2 ) is changed Into "the year of Yahweh's favor"; "Do I now persuade men" ( Galatians 1:10 ) into, "Am I now seeking the favor of men," and there are other the Revised Version (British and American) changes.