This question is the subject of some controversy lately because some of the traditional explanations have been disputed by recent scholars. These traditional explanations tended to emphasize things like the backwardness of the native peoples who believed that the Spaniards were gods.
Modern explanations tend to look at the following two major factors.
First, they look at the technological advantages that the Spanish had. The fact that the Spanish had steel weapons and armor was a huge military advantage. This advantage was multiplied by the psychological (and to some extent military) advantage gained by having guns and horses since neither of those things was familiar to the native people.
Second, they look at the fact that the Spanish often had allies among the native people. This was especially true in Mexico where the Aztecs had many bitter enemies who chose to side with the Spanish against the Aztecs.
Overall, then, current explanations tend to emphasize the help the Spanish got from their technology and their native allies.