The verse concerning Joseph's famous coat of many colors is found in Genesis 37.
Now Israel (Jacob) loved Joseph more than all his children, because he was the son of his old age: and he made him a coat of many colors (Genesis 37:3, King James Bible).
Not What You Think
There are two keys words in Genesis 37:3 that reveal the truth behind the "coat of many colors." The first, kethoneth (Strong's #3801), is translated as "coat" in the King James. The second, pas (passim, Strong's #H6446), is translated "of many colors."
Strong's Concordance and Brown-Driver-Briggs Hebrew Definitions defines kethoneth not as a cost but as a tunic. Additionally, the Hebrew pas (passim) has nothing to do with color. It means something worn, like a tunic, which is long (to the ankles) and which has long sleeves (to the wrists or palm). Some Biblical commentaries confirm this conclusion.
"But in truth it was not a "coat of many colors," but a tunic reaching down to the arms and feet, such as princes and persons of distinction wore, and it betokened to Joseph's brothers only too clearly . . . " (Bible History Old Testament).
"The references to Joseph's coat of many colors (Genesis 37:3, 13, 12) and "garments of divers colors" (2Samuel 13:18 - 19) probably do not mean the color of the garment at all, but the form . . ." (International Standard Bible Encyclopedia).
"The more luxurious classes of society - e.g., women of royal blood (2Samuel 13:18 - 19) and men of leisure - wore tunics with sleeves. This is the meaning of the Hebrew "passim" occurring in the description of the garment presented to Joseph by his father (Genesis 37:3). It was not "of many colors" . . . the color of the shirt worn even by those of high rank was yellow, or red, or black." (1906 Jewish Encyclopedia article on Coats).
At least eleven of twenty-five Bibles (including the New International Version, Young's Literal Translation and the Holy Bible Faithful Version) do not mention any colors in their translation of Genesis 37:3.
Favoritism
What made Joseph extra special to Jacob such that the patriarch favored him above his other eleven sons and one daughter?
Joseph's birth, when Jacob was 91, was through his beloved and favorite wife Rachel (Genesis 29:17 - 18, 30). He was the firstborn son he greatly longed for as God allowed his three other wives (Leah, Bilhah and Zilpah) to produce children before Rachel (Genesis 29:31, see also 29:31 - 30:21).
Joseph also reminded his father of Rachel who had died less than a year prior while giving birth to Benjamin (Genesis 35:16 - 20).
Lastly, Jacob felt justified in gifting Joseph a "coat of many colors" since he had comforted him in his old age. He proved he was a useful and faithful son to his father (Genesis 37:2) who behaved wisely for his young age.
Symbolism
What did Jacob's gift symbolize?
"The working classes usually wore a short tunic, whereas the aristocracy wore a long tunic with long sleeves. Thus it would be a mark of distinction for Joseph to wear the latter" (Manners and Customs of Bible Lands).
A long tunic with sleeves would be impractical and get in the way of strenuous work such as farming or herding. Jacob's gift was meant to show he wanted Joseph to help supervise and oversee his wealth with him. It also hinted at the elevated status he would achieve thirteen years later when he becomes the second most powerful person in the Egyptian Empire (Genesis 37:5 - 11, 41:39 - 46).
Jacob's special love of Joseph, however, did not end with his special gift of a "coat." The patriarch, just before his death at age 147, placed his name (Israel) on Joseph's sons Ephraim and Manasseh (Genesis 48:13 - 20). This act, along with further blessings, destined the two tribes to be leaders within Israel (49:22 - 26).
Conclusion
The "coat of many colors" was, in spite of what many people have been taught, an expensive tunic in one color. An accurate translation of the verse in question is the following.
And Israel (Jacob) loved Joseph more than all his sons because he was the son of his old age. And he made him a tunic reaching to the soles of his feet (Genesis 37:3, HBFV).