what led to the relatively rapid conquest of the caribbean and mexico?

Answer 1

the spanish brought disease with them which the indigenous people had never been exposed to (small pox, influenza, etc.) and this wiped out some of them pretty rapidly. also, the spanish had guns, horses, better technology.

but mostly, the spanish had come out of a time in europe after the spanish inquisition had tainted everything with religious righteousness/zeal and the lust for gold, wealth, empire. so the spanish came with two things in mind - increasing wealth and power and spreading christianity, by any means necessary. the indigenous people (especially the smaller tribes) mostly lived in communal societies and were not prepared for this type of ruthlessness and were therefore often caught off guard by teh massacres and mass enslavement by the spanish.

Answer 2

Better technology, ships, guns. And a different values system.

Answer 3

disease and pestilence wiped out hundreds of thousands, if not millions.