The word jihad can mean a crusade or struggle, and comes from the holy war of Islam directed against all that defied the word of God as written in the Koran. The equivalent of jihad can occur in any society brought to a peak of emotion by religious fervor or other means. The value of the jihad to society is that the people caught up in the emotion of the enterprise place their best interests, even their lives, second to the purpose of the crusade. The jihad was especially effective at a most desperate time when survival of the group hung in the balance.
—Age of Empires manual
Jihad in Arabic literally means "struggle", viz (in Islam) "striving or exerting oneself for God". It can have different shades of meaning, like betterment of oneself and society, though sometimes it is misunderstood to exclusively mean religious warfare, and is strongly associated with extremist groups.
In the Definitive Edition, the name may have been changed to Zealotry in order to shake off these misconceptions and in part because of the negative connotations surrounding the term.