To understand the how issues in the Middle East affect terrorist attacks around the world, you need to understand some of the history of the area. The struggle for the property promised to Abraham and his descendants in the Old Testament has brought trouble to the region for 5,000 years. Since the time when the first born son of Abraham, Ishmael, was sent away to make room for Isaac, conflict between the descendants of the brothers has been a problem.
Today, these two people groups are filled with resentment and hatred for each other in the Middle East. Additionally, in 1948, when Israel displaced those who already were settled in the land that Israel now occupies, it only increased the feelings of hostility. The conflict was mostly restricted to the local area around Israel until after the 1967 and 1973 battles that ended with Israel occupying even more Middle East real estate.
It had become apparent that the defeat of Israel in straight head-to-head battles was not likely to be a short term possibility. Various terrorists groups began to emerge with violence in other parts of the world. Most of these claimed to either be a part of the Middle East groups or to be working with them. The terror acts were directed at places and people who were friends and allies of Israel. These attacks ranged from hijacking ships to planes; bombing cars, trains, and public places; and culminated with the attacks on 9/11. It is likely that they are not over.
The Qur'an espouses the spread of Islam even with violence in some circumstances. This has been interpreted by the more radical Muslims as an endorsement for creating strife in other parts of the world. This has resulted in a lot of the problems in various African nations. While not all African violence can be attributed to this, much of it can. This is especially true in lands where there are strong Muslim and Christian cultures existing in close proximity.
Israel is sometimes at the heart of certain terrorist activities. Most of this is blamed on efforts at self-defense against the Arab nations and extremists. However, some Israelis resent the existence of the Islamic nations that surround them as much as the Muslims resent Israel. Because of this, extremists from Israel work to keep the fires hot by doing acts of terrorism against Muslims and Palestinians in the Middle East and elsewhere in the world.