Jihad means "Holy War"
This has, undoubtedly, become the popular Western definition of the word. It is partially correct, but it is little known that jihad actually means "strive". Jihad comes from the Arabic word jahada which means "to strive", or "to struggle" (against external forces). The root of the word, juhd, means "effort". Therefore, jihad simply means "exerting one's best effort", and encountering some form of "struggle" or "resistance", in order to achieve a specific goal. The word jihad can also be used in a generic sense, to mean "exerting the best efforts against something", even if that goal is not related to Islam. Even the Qur'an uses the verb jihad in non-religious contexts (see Surah 29:8 and 31:15).
The Qur'an also uses the term jihad specifically in the sense of "struggle/effort for the sake of Allah". Although this can mean fighting with arms, it also means resisting the evil drives and desires in one's self. And so, there are two types of jihad. The "greater jihad" is a 'spiritual' type. It means the inner struggle a believer has, to do the right thing, and resist evil. The "lesser jihad" is that of religious warfare. This "lesser jihad", or "armed jihad" is a response to armed agression, and is only temporary. The "greater jihad" is permanent, because there are always causes for it - one is always struggling against one's own weaknesses. This peaceful jihad can refer to anything instance of peaceful struggle undertaken by a Muslim against external forces, such as preaching in a hostile environment, opposing an evil act, or even donating money to the poor - because it involves struggling against one's selfish desires to keep one's money for one's own pleasures.
So, even though jihad can mean "holy war" - or rather resistance to armed agression - it is actually meant, first and foremost, to denote a believer's inner spiritual struggle.