I suspect the Mongols tearing through the Islamic world, including sacking the heart of Islamic civilisation and massacring a vast proportion of its population, had a not inconsiderable impact.
The origins of terrorism are geopolitical. Terrorism is effectively the way the weak fight back militarily. That's one aspect of terrorism, such as Al-Qaida or ISIS in the Middle East. It has direct political aims to achieve, and believe terrorism is an effective tactic to achieve that. Very little of this goes on in the West, because there is so little to achieve with it in the West.
Some of it is just violent people with an urge to kill, but humans are rational creatures and so also like to rationalise violence. Religion can provide an excuse as easily as anything, and there is an established logic from the above form of terrorism. But I'm not sure this is really any different from all the other thugs and murderers out there who indulge themselves with some sheen of reasoning.
Then there are the "crazies". In Indonesia, people would "run amok" with a knife or sword. In the USA, they "go postal". And equivalent Muslims go on a suicidal religious killing spree. It's not about a particular grievance; a grievance may provide a superficial excuse, but it's really just a way people snap and decide to go down in a blaze of destruction, as they have done everywhere since forever. So perhaps we call this terrorism, but in truth it sort of isn't. It's just self-destruction as a futile attempt to find meaning and certainty.
