What does "The Compromise of 1877" represent when we talk of African American history?
With respect to African American history, the Compromise of 1877 represents how, once again, the rights and interests of African Americans have been ignored by whites when that has been convenient.
The Compromise of 1877 was the political bargain that ended the Reconstruction Era. In 1876, Rutherford B. Hayes ran as a Republican in the presidential general election while Samuel Tilden ran as the Democrat. The Republicans were the party of Reconstruction. In part because of that, and because of lingering animosity from the Civil War, the Democrats dominated the South. The election was very close, and there were numerous conflicts about the legitimacy of the vote in various states.
Because of all this, the election ended up being decided by an electoral commission. The commission had a very hard time deciding who to announce as the winner. So a compromise was, apparently, reached. If Hayes would be selected as the winner, the Republicans would agree to end Reconstruction. This was the Compromise of 1877.
With the end of Reconstruction, the hope of black rights in the South died. This shows that whites in power in the US were willing to sell out the rights of African Americans is that was what was politically convenient.