How did the division in the Inca and Aztec empires help the explorers?

Both Empires consisted of a 'master' people that had over time established their territory by subjugating other peoples. The Conquistadores made use of the fact that amongst those peoples there would always be some whose leaders hoped to gain power or independence for their tribes by helping the Conquistadores bring down their 'oppressors'.

Despite their vastly superior weaponry, horses and pure bloody-mindedness the Conquistadores could never have brought down the Empires single-handedly because of their small numbers. In the case of the Incas, a lot of double crossing made them need only limited help from subjugated peoples. In the case of the Aztecs, these peoples provided the Spanish troops with a formidable auxiliary force that they used to defeat the Aztec forces.