"Coat of Many Colors" is a mistranslation. According to the highly-respected eleventh-century scholar Muhammed Ibn Ibrahim Al-Thalabi, the original words were "garment with marks." (One of the King James Bible translators added the word "many"). It is not certain what the "marks" were or what they represented. Some scholars believe that the garment may have been a symbol of Jacob's position as High Priest of the tribe, and that the older brothers were angry because Jacob chose to pass them over and give Joseph the priesthood instead of them.
Joseph's tendency to have prophetic dreams was a characteristic also given to Jesus's father Joseph. Joseph's father's name is Jacob, which was also the name of Jesus's brother, although most English-language translations change his name to James.
Although the English Bible describes it as a 'coat of many colors,' this was actually the result of a translator's replacing the original expression with one that he devised. In fact, it is not known exactly what made Joseph's coat so special - perhaps it bore the colors of his clan.
The original West End production opened in 1972. The Broadway production of "Joseph and the Amazing Technicolor Dreamcoat" opened at the Royale Theater on January 27, 1982, ran for 747 performances and was nominated for the 1982 Tony Awards for the Best Musical, Book and Score.