Jihad is struggle for justice against oppression, a fight against evil by the masses, even by rebellion or armed resistance. The Harkonnen and the Emperor's Sardaukar are seen as oppressors, and the Fremen (especially the Fedaykin), use armed resistance against them. This is labeled by Frank Herbert as Jihad, and is very close to the real meaning of the concept.
A Jihad is a verb meaning to "struggle" or to "strive". One can have an internal jihad, family jihad, or religious jihad, which may or may not include violence towards non-Muslims. A comparison may be made with the term "crusade", which is sometimes considered by Muslims to mean Western violence against Islam, when it is more often used as a metaphorical struggle; for example, "a crusade against drugs". However, Jihad can refer to a holy war, in the sense that it is ordained by God and is the only kind of warfare not considered a sin in Islam. The aim of such a religious jihad is not to convert non-Muslims to Islam but rather to defend the Islamic state.
Paul Atreides sees the jihad in some of his earliest prescient visions, and struggles to find a way forward that will not ignite the conflict throughout the universe. He fails, however, as when he achieves victory, the Fremen move forth throughout the universe, bringing "The Peace of Muad'dib" with them, forcing their religion on billions by the sword.
It should be remembered also that in Dune, Jihad is not solely associated with Islam, or religion as a whole. As in the case of the Butlerian Jihad the use of the term Jihad was used to describe the plight of humanity as a whole.