“Cursed be Canaan” was the malediction that Noah pronounced on Ham and his descendants. Ham, because he looked upon his father’s nakedness, was cursed. As you recall, Shem received a patriarchal blessing, and an enlargement of that was given to Japheth. One is the fact that Noah had three sons, Shem, Ham, and Japheth.
Usually two biblical texts are drawn upon to support that view. Some people insist that the Bible meant for the races to remain pure, therefore prohibiting any kind of interracial marriage.