What describes that the president Ruthford B Hayes and his administration are best known for

Ending the Reconstruction era.

Rutherford Hayes met in secret with moderate southern Democrats in order to negotiate acceptance of Hayes' election. The Democrats agreed not to block Hayes' victory on the condition that Republicans withdraw all federal troops from the South, thus consolidating Democratic control over the region. As a result of the so-called Compromise of 1877 (or Compromise of 1876), Florida, Louisiana and South Carolina became Democratic once again, effectively marking the end of the Reconstruction era.

End of Reconstruction