The Quran does call for "jihad" as a military struggle on behalf of Islam. But the Quran also refers to jihad as an internal, individual, spiritual struggle toward self-improvement, moral cleansing and intellectual effort. It is said that Prophet Muhammad considered the armed-struggle version of holy war "the little jihad," but considered the spiritual, individual version of holy war--the war within oneself--as "the great jihad."
Including the "jihad" as one of the five pillars of Islam is another common Western misunderstanding. Jihad is not among the five pillars of Islam (the profession of faith, prayer five times a day, fasting during Ramadan, alms for the poor and performance of the Hajj, or pilgrimage to Mecca, at least once in each Muslim's lifetime).
Still, "jihad" is considered to be every Muslim's duty--be it the struggle to improve society, preventing the exploitation of the poor or vulnerable, or improving oneself before the Day of Judgment.
Several militant or political Islamic organizations have adopted the term in their monikers. These include Egypt's Jamaat al-Jihad community, established in the late 1970s by militant Sunnis and responsible for the assassination of Egyptian President Anwar Sadat in 1981; Islamic Jihad, an offshoot of Hezbollah in Lebanon and used since 1982 in covert military activities; and Palestinian Islamic Jihad, which has conducted suicide attacks on Israeli targets. All three groups are on the U.S. State Department's list of Foreign Terrorist Organizations.
See also: Mujahid or mujahidin.