What does Al Qaeda want from us? Why are these people under such enormous social and cultural pressure to fight us?
In a nutshell: Al Qaeda is comprised of religious fanatics who want the entire world to convert not only to Islam, but their extremist brand of Islam. That's the ultimate goal. America is an immediate goal, as America is a representation of all that is wrong in the world.
Fighting America and her allies is for them reminiscent of Saladin fighting the Crusaders for the Holy Land.
"Reason obeys itself; and ignorance submits to whatever is dictated to it" -- Thomas Paine