They were also known as the Albigensians, after the city of Albi (which I visited on my hols) and were linked to the Bogomils of eastern Europe, the Gnostics of the late Classical period, and the Manicheans of the Middle East.
Their view was that the material world in which we are embedded is an evil trick, from which we must free ourselves. Failure to free yourself means you will continue to be bodily reincarnated. The Cathars were known in the Middle Ages for their simplicity and purity.
The Inquisition destroyed the Cathars in the most bloodthirsty way, basically by murdering and torturing them all. The Cathedral of St Cecile at Albi was built to affirm the Church's domination of the region. It is a horrifying building in every way. It is a massive brick-built fortress, and apparently it stands on extensive dungeons, though visitors don't have access to them.
The other striking thing about the Cathedral is that inside there is a tall blue frieze depicting naked men and women being tortured in various repulsive ways by lascivious demons. No kid. It was created by Flemish artists in the 15th century, and resembles Bosch or Breughal, but in a less sophisticated style. You have to see it to believe it. The distorted sexuality and cruelty of the scene would make your hair stand on end.