I assume that you are asking this question about the chapter that David Cahill wrote in Questioning Collapse, edited by Patricia McAnany and Norman Yoffee. In that chapter, Cahill explores the reasons why the Inca Empire fell to the Spaniards. The crisis that Cahill talks about was an internal crisis that was brought on by Incan imperial policies.
When the Spanish arrived in Peru, the Incan Empire was very strong. It had expanded by conquest and had taken power over a number of peoples who were now its subjects. Many of these peoples had been conquered relatively recently. Cahill argues that this meant that the subject peoples were not happy being under Incan domination.
This was the crisis that the empire faced. It had many groups within its territory that hated it and wished to overthrow it. When the Spanish arrived, these groups came to have some hope of succeeding in overthrowing the Inca. As Cahill says on p. 226,
Once the Spaniards’ aggressive intent became apparent, however, the possibility of alleviation or liberation from the reach of Cuzco and its attendant burdens was immediately grasped by the Incas’ forced “allies…”
These erstwhile “allies” of the Incas turned against them, helping the Spanish militarily and in other ways. This was instrumental in allowing the Spanish to conquer the Inca.
Thus, the crisis was one of internal dissension. The presence of disgruntled groups within the empire greatly helped the Spanish to conquer the Inca.