Jefferson Davis had been one of two US Senators from Mississippi in 1861, when he resigned to become the President of the Confederacy. During the Civil War, neither the North nor the South attempted to name a replacement. After the war, Mississippi went under Military rule, which did not believe it had the authority to name a Senator. In 1870 this ended and Civilian rule was restored to Mississippi. Given that Davis had been elected Senator in 1860, his seat came open for election in 1866 and then again in 1872. In 1866 the Military government did not think it could elected a Senator (Remember this is under the old rules, when Senators were elected by the State Legislature NOT by popular vote). In 1870, Civil rule restored, the state Legislature looked for someone to "fill in" the seat till the next election cycle of 1872. Revels was elected by the State Legislature by a vote of 81 to 15 and was seated in the US Senate by a vote of 48 to 8.
http://en.wikipedia.org/wiki/Hiram_Rhodes_Revelshttp://statelibrary.dcr.state.nc.us/nc/bio/afro/revels.htm