Islamic term, Arabic for 'battle; struggle; holy war for the religion'.
Jihad has two possible definitions: the greater, which is the spiritual struggle of each man, against vice, passion and ignorance. This understanding of jihad has been presented by apologetics of modern times, but is an understanding of the term rarely used by Muslims themselves.
The lesser jihad is simplified to cover holy war against infidels and infidel countries, aiming at spreading Islam. This kind of jihad is described in both the Koran and in the hadiths.
Koran sura 9: Repentance
41 March ye then, light and heavy, and fight [jāhidū] strenuously with your wealth and persons in Godís way; that is better for you if ye did but know!
Muslim law has divided the world into two entities, dar al-islam, the abode of Islam, and dar al-harb, the abode of war. Battling against the Abode of war was a duty for a Muslim, as this is the only way for the peace of Islam to take the place of the warlike conditions of the infidels' society. Jihad can be both defence, as well as attacking an enemy.
The enemies of Islam are divided into two groups, the Peoples of the book, ahl al-kitab and the pagans, the kafirun. The first group, defined as Jews, Christians, Zoroastrians, and Mandeans need only to submit to an Islamic ruler, and live in peace with other Muslims to end the situation where jihad is imperative.
For the pagans there is a principle fairly similar, but they get less rights under the Muslim ruler than the Peoples of the book. While this group generally can live safely inside a Muslim society, some Muslims have propagated that these should either convert to Islam or face death penalty. In situations where the Muslim rulers mean that war has to be waged against the infidels, they should be allowed sufficient of time to convert before the Muslim army attacks.
Jihad is a duty for every Muslim community, but not necessarily for every individual: it's sufficient that a certain number of the able men perform jihad. The one who dies in the battle against the infidels, becomes a martyr, a shahid, and is guaranteed a place in Paradise as well as certain privileges there.
While offensive jihad, i.e. attacking, is fully permissible in Sunni Islam, it is prohibited for some of the larger groups of Shi'i Islam, which consider only the Imam, now in occultation, as carrying the right to decide to go to war or not.
The Kharijis regarded jihad as the sixth pillar of Islam, a position that other groups of Islam have adhered to earlier.