And the LORD set a mark upon Cain. - Genesis 4:15
Until the 1978 revelation to Mormon President, Spencer W. Kimball, black men were not allowed to hold the priesthood. This was based, in part, on Genesis 4:15, where God placed a mark on Cain after he had killed his brother Abel. Joseph Smith and later LDS leaders interpreted the "mark upon Cain" to be turning of Cain's skin (and that of all his descendents) black.
It should be noted, however, that Mormons were not alone in this interpretation of Gen.4:15. Many Protestant denominations at the time Joseph Smith founded the LDS Church (1830) had the same racist understanding of the "mark of Cain." (See link 3)