Answer: To intimidate blacks and maintain white supremacy in the South.
Details:
The Ku Klux Klan began in 1866 in Tennessee as an organization of Confederate veterans of the Civil War. They derived the name "Ku Klux" from the Greek word κύκλος (kuklos) , which means circle. The group became a resistance movement against radical Reconstruction in the South, seeking to intimidate blacks and restore white supremacy. The group carried out many acts of extreme violence, and acts in Congress and a decision by the Supreme Court (United States v. Harris, 1882) went against the Klan. By that time, though, the Klan had mostly stopped operating because it had pretty much achieved its goal: white dominance in the South.
A revived version of the Klan appeared again beginning in 1915, expanding its target beyond blacks to Jews and others. At its height in the 1920s, this revived version of the Ku Klux Klan had more than 4 million members. Today it is a fringe group in the US, with only a few thousand members.