What were the religious, political, and economic motivations behind the Crusades?
The religious motivation for the Crusades is the one most people know about: Europe was predominantly Christian and ruled by Christian governments while the Middle East was predominantly Muslim and ruled by Muslim governments. People in each religion believed (as many still do today) that their religion is the one true religion and everyone else's religion is wrong; furthermore, a substantial proportion believed that those who do not believe the right religion should suffer or even be put to death. Thus, there were a large number of Christians willing to kill Muslims simply because they were Muslims, and conversely a large number of Muslims willing to kill Christians simply because they were Christians.
But that is not the whole story of the Crusades.
There was also a substantial political motivation; European governments found that by launching wars and conquering territory in the Middle East they could strengthen their own power at home. In particular, the Catholic Church used the Crusades as a means of uniting all Christians in Europe under one banner and solidifying the authority of the Church in public life. There were strategic reasons to establish military footholds in the Middle East, particularly as a bulwark against the rise of Turkey.
Finally, there were economic motivations. The Middle East has always been a region very rich in natural resources (today we think in terms of oil, but back then petroleum was basically useless; they were more interested in precious metals like gold and silver, as well as simply rich farmland and comfortable living space). European governments reasoned that by capturing territory in the Middle East they could secure access to these natural resources and thereby make themselves wealthier. To some extent this was true, though they probably would have actually made more wealth by trading peacefully with Middle Eastern cultures rather than going to war to conquer them.