Primarily, the acts of terrorism are motivated by the ideology that this world is a temporary place to live and the afterlife could be much more rewarding. Most terrorists believe that they will enter the paradise where they will get 72 virgins to have sex with and unlimited fruits to eat, and to live a life full of glory and unlimited bounties.
Indeed, this is the idea that simply motivates their acts of terrorism while interpreting the Quranic verses to an extreme level. Following their extreme interpretation, they believe themselves to be on the path that God has commanded them to follow.