In the High Middle Ages, Clan MacDonald was by far the largest and most important clan in the Scottish Highlands, to the point that the chieftain of the clan was able to call himself the "Lord of the Isles." As the seat of Scottish power was located in the southeast of the country, in the lowlands, while the Lordship of the Isles spanned mainly the north and west and the islands, the Lords of the Isles were essentially operating independently of the Kingdom of Scotland.
Clan Campbell had humbler roots. Their base of power was located on the Scottish mainland, in the region of Argyll. They spent the Middle Ages being a fairly minor clan, but when the Reformation came to Scotland, they saw a chance and took it, becoming one of the first clans to convert to Protestantism. Unlike the MacDonalds, who had defied governmental rule, the Campbells instead attempted to achieve power through working with the Scottish (and, later, British) government.
The MacDonalds, meanwhile, were losing their power in the west of Scotland. Prior to the early 17th century, there had essentially been a fairly unified Gaelic cultural region that transcended political boundaries, taking in land from the southwestern tip of Ireland to the Outer Hebrides. The MacDonalds had been key power-holders in this region, with several members of the clan settling in County Antrim in Ireland and forming the McDonnell sub-branch. However, this came to an end when James I/VI, in one of his first acts as British King, decided to split the region by planting non-Gaelic settlers from mainly lowland Scotland in the province of Ulster in Ireland to block easy communication. These became known as the Ulster-Scots, or the Scots-Irish, as their American descendants are called. (James tried a similar thing on the isle of Lewis in the outer Hebrides, but this failed.) The united Gaeldom was no more. Now the MacDonalds were largely stuck in the western corner of a region that was beginning to be targeted aggressively with British government policies.
The recent Campbell ascendancy essentially meant that there were two spheres of influence in the Highlands--the Catholic MacDonalds, and the Protestant Campbells. And, increasingly, a cycle developed wherein in conflicts the Campbells took the side of the British government, the British government usually won, and the Campbells reaped the benefits. The clan's wealth can be seen in the 18th century construction of Inveraray Castle, by far the most palatial, modern clan seat in Highland Scotland (and where the chief of the clan, the Duke of Argyll, lives to this day). This wealth and status also generated resentment against the Campbells from many of the other clans.
The most famous Campbell/MacDonald altercation was the massacre of Glencoe, in which a sept of MacDonalds were attacked by a party of British government soldiers they had been hosting, many of whom were Campbells. The reason for this was that the chieftain of the sept had been late in signing an oath of allegiance to the King at the time, William III. The massacre of Glencoe is often characterized as a purely clan-based fight, but in reality the truth is more complex--the mastermind of the attack had been a lowland nobleman who wanted to make an example of the MacDonalds, and the Campbell general who was commanding the government force seems to have had reluctance to commit the act. However, the attack became a major propaganda piece for Jacobites in the 18th century, who argued that this was an example of governmental oppression that would be alleviated with the return of a Catholic Stuart on the throne.
The Jacobite rebellions, particularly the second one in 1745, demonstrate clearly the political conflicts in the Highlands. On the government side was the Campbells, and a few other clans such as the MacKays. Key rebel clans included the MacDonalds, the Camerons, the MacLeans, and the Frasers. (A few clans, such as the MacKenzies and MacLeods, chose to remain neutral.) Ironically, the fact that the Campbells had taken the winning side meant that they were allowed to continue several Gaelic cultural traditions that were banned for the rebelling clans. Of course, most Americans probably know the names now more as a fast food chain and a canned soup brand more than anything else.
(Fun fact: members of Clan MacDonald were frequently given the first name of "Raghnall," which is the Gaelic version of the name "Ronald." That's right, there were lots of real-life Ronald MacDonalds walking around the west Highlands in the Jacobite days.)