Trying to avoid overly political answers, but obviously what people mean by jihad has been quite a loaded term. People use it to describe contemporary acts of terrorism, the early conquests of the Islamic Caliphate, or as a kind of internal struggle to achieve piety. Just wanted to get the historical perspective of what this word meant, especially early in the history of Islam and whether the meaning behind the word has changed since then.
This is actually a tricky question because we don't have that many sources from the first couple centuries after the death of Muhammad. What we do have are sources starting really in the 9th century that claim to collect oral traditions and give citations to older texts that are not available to us today. Then we have to deal with the fact that these texts fall in a number of different genres, each with their own intentions and audiences.
So, let's break this down the way most modern historians have tended to approach a topic like this. First, what does the Quran say? Well, for the most part, when the Quran uses the word jihad or its derivatives it never means unambiguously fighting. Examples include 25:52 - "So obey not the unbelievers, but struggle with them thereby mightily." (wa-jahidhum jihadan kabiran) which could imply that you should struggle to not obey laws that force you to go against Islam or 22:78 - "Struggle for God as is His due." (wa-jahidu fi llahi haqqa jihadihi) again very ambiguous in what that struggle means. Just like all holy texts, the Quran does have a lot of fighting and violence. In those instance where the Quran is speaking unambiguously about violence it uses terms like qatala/to fight or kill or haraba/to fight or make war. On top of this, it is those passages which discuss fighting and violence where you run into the most issues with abrogation (verses that appeared later overruling earlier verses when they contradict each other, of course, this is easier said than done since the Quran is not arranged chronologically and there some disagreements about which verses came first and which came last). For a fuller discussion of this issue, see Reuven Firestone's Jihad: The Origin of Holy War in Islam (1999).
The ideas of the inner or greater jihad others have mentioned in this thread can be taken from the Quran but they are not fully developed by Muslim jurists until much later.
Second you would look at what the hadith say. Many collections of hadith, all of which claim to capture an oral tradition that goes back to the Prophet Muhammad but are only written down starting in the 9th century (the earliest of the accepted collections of sound hadith is that of Malik who died in 795, the next is that of Bukhari who died in 870), include a book of jihad that focuses on the rules of war and combat. The earliest surviving religious treatise specifically on jihad we have available to us is Ibn al-Mubarak's Book of Jihad (he died in 797). Most important here is an emphasis on the rules of war and the necessity of proper leadership in conducting jihad, pretty much all of which modern jihadist groups ignore. Many of the early writers on jihad focused much of their attention on the proper conduct of war along the Byzantine border.
Next we can look at chronicles and historical texts. The history of the Arab conquests are very difficult because, again, the existing sources emerge centuries after the fact and they do not make clear the rationales behind the conquests. Therefore we have many different interpretations. The contemporary sources we do have are those of the people the Muslims conquered and those do not show a faith being spread by the sword or a clear religious motivation for the conquests, the emphasis is more on collecting tribute and taxes. Where jihad does really emerge in medieval chronicles, histories, etc., the emphasis is clearly defensive or, in the case of warfare with the steppe Turks in Central Asia, a preemptive form of defensive warfare.
Over the centuries, the meaning has clearly changed. During the Crusades, for example, Nur al-Din and later Saladin employed small armies of religious scholars whose job was to revive the notion of jihad (it had mostly gone by the wayside because the collapse of the `Abbasid Caliphate and successive waves of Turkish invaders had made the classical formation of jihad invalid) and incorporate it in a propaganda that legitimized their rule as those who were leading the fight against the crusaders (and, to a lesser extent, the Shi'ite Fatimids in Egypt).
I know your original question is meant to focus on the use of terms like jihad today and you clearly see a new development in the last few decades. For the most part, modern jihadist movements fail to meet even the simplest rules of conduct set up by a classical formulation of jihad starting with not meeting the criteria of having a leader who is recognized by the Muslim community as some one educated in Islamic law and traditions to violating injunctions against harming civilians, especially women and children, and protections from non-Muslims all the way to engaging in takfir (accusing Muslims of not being real Muslims) and killing fellow Muslims (the largest target of modern jihadist movements are their fellow Muslims). These ideas are purely modern in their construction.
Anyways, if you want to read more about the history of the term, I would recommend a couple of good books. My favorite, for a quicker read, is Michael Bonner's Jihad in Islamic History. I would add to that list David Cook's Understanding Jihad and Reuven Firestone's Jihad: The Origins of Holy War in Islam.
Within the context of the classical Islamic law, it (Jihad) refers to struggle against those who do not believe in the Islamic God (Allah) and do not acknowledge the submission to Muslims, and so is often translated as "Holy War". It most likely pertained to this area of meaning, as the first couple hundred of years of the beginning of Islam marked years of perpetual war. In fact, Khalid ibn al-Walid, one of the greatest generals in history, was a companion of Muhammad, and later general for Abu Bakr. He was victorious in over a hundred battles (so the writings say), in which he never lost one. Regardless of how many he won or if he did lose, there is no doubt that Muslims quickly conquered a lot of holdings under Byzantine influence, and conquered Sassanid Persia.
That being said, talk of jihad can have two meanings: an inner spiritual struggle, the "greater jihad"; and an outer physical struggle against the enemies of Islam the, "lesser, jihad"which may take a violent or non-violent form. Jihad is very important to muslims, and some even consider it an unofficial pillar of Islam, as Jihad is closely related to a Muslim's 'religious duty'. Islamic historian Bernard Lewis has stated that "in the large majority of cases, Jihad has pertained to martial acts." The term of Jihad has not really changed much in the years, and truthfully has mostly been military action through religious justification. However, it is a complex thing to understand to outside cultures; consider the fact that 'Islam' itself means submission (to Allah), thus Islam is more than a religion, it is also a lifestyle, and one taken much more seriously than what people take modern Protestantism and Catholicism in most countries do to this day.
Jihad means to strive and struggle for purification. There is a difference between jihad and Qital and you can find a good post here http://jihad.info/difference-between-qitaal-and-jihad.html
The most acceptable meaning of Jihad is to struggle and strive. It is not what you see or hear in media these days. Some people Khawarji is the terms in Arabic have hijacked Islam and using their terror tactics to conquer the land and oil rich countries. More on jihad can be found on jihad.info a website setup to counter attack ISIS and TAliban