I dont think they really want anything, They get off on the power to frighten and commit heinous acts.
They are people with small minds who think their act will bring them some sort of fame.
Their leaders get off on knowing that their followers are stupid enough to do their bidding.
A very dangerous misperception, I think. Don't be fooled by what we (Americans) would perceive as a personal "power trip" without a larger motive. Yes, it's a lust for power, but there is a large segment of the "jihadist" community that truly has the destruction of America and the institution of Islam worldwide as its open goal.