The black priesthood ban fall would come from pressure by the U.S. Congress and from problems determining whether or not a person in Latin America was eligible to hold the priesthood, especially when the temples started to be constructed.
The full fall of the priesthood ban took place over a period of many decades, but in 1979, President Spencer W. Kimball announced that the time had come for blacks to hold the priesthood and an official declaration was placed at the end of the Doctrine and Covenants.
Although there were political pressures and monetary concerns that may have contributed to the announcement, the declaration was given in theological terms. After the ban was lifted, many blacks were ordained into the priesthood.
Read more: "Mormonism's Black Priesthood Ban: People of African Descent Were Not Able to be Ordained until 1978" -
Mormonism's Black Priesthood Ban: People of African Descent Were Not Able to be Ordained until 1978