The Black Legend was the idea that the Spanish had acted in particularly cruel and evil ways in their dealings with the Indians. It has come to include the idea that the Spanish were much worse than other colonial powers. Please note that it was not the Indians who spread the "Black Legend." This was something that was done first by some Spaniards and then by other Europeans.
The Black Legend can be said to have started with the writings of Bartolome de las Casas. He was a Spaniard who was the bishop of Chiapas in what is now Mexico and was a strong defender of the Indians. He alleged that they were being terribly mistreated by his countrymen.
These writings were picked up and then exaggerated by Europeans who had reason to want to make Spain look bad. In particular, this included the Dutch (who were trying to break away from Spanish rule) and the English (who were competing with Spain for colonies in the New World). These two European nations had an interest in making Spain look evil in the eyes of the world to justify their struggles against Spain and to rally support for those struggles.