Not sure I agree with the premise that British Army casualties during Operation Banner were 'high' — that's a relatively subjective evaluation, and one that's subject to interpretation. To my mind, 722 deaths as a result of 'terrorist action' (the British government's categorisation, not mine) over the course of a counter-insurgency campaign which lasted 38 years is a relatively low death toll.

In any case: your question is immensely broad, and so difficult to answer concisely. There's already been a lot written about the Troubles, but the historiography is nonetheless relatively nascent.

Among other things, oral history efforts like Boston College's Belfast Project are causing political scandals because many participants in the Troubles are still alive — and so can potentially be prosecuted for crimes committed during that era. There are also large quantities of UK government files from the last phase of the Troubles which are yet to be released under the 20-year rule — and many more, from the military and intelligence services, which won't be declassified for many years to come.

But, those caveats aside, here's my attempt to give a brief overview of the context and causes of the Troubles:

The Troubles find their roots (you could argue that they were a successor conflict) in the painful process of Ireland becoming independent from Britain.

In 1920, the fourth Home Rule Act divided Ireland into 'Southern Ireland' — which became the Irish Free State with the Anglo-Irish Treaty of 1922, and then the Republic of Ireland later — and 'Northern Ireland' (comprising most of the Province of Ulster). There's a significant sectarian component here: Northern Ireland differs from the rest of Ireland in that it has a Protestant-majority population.

Northern Ireland opted out of the Anglo-Irish Treaty; it elected to remain part of the United Kingdom. That partition was — and remains — anathema to Irish republicans. The ultimate objective of the Provisional IRA's armed campaign (and that of the other republican paramilitaries) was the reunification of Ireland — ie. the incorporation of Northern Ireland into the Republic of Ireland.

Northern Ireland was, and remains, a deeply divided society on this issue. The general, glib explanation is Protestants = Unionists; Catholics = Republicans. That's facile (it is the case that most unionists are Protestants, and most republicans are Catholics, but that's not quite the same thing), and there's plenty of academic debate about the role of religion in the conflict, but sectarianism is certainly one crucial dynamic in explaining why what is fundamentally a political question became such a violent, socially divisive debate.

So, that's the historical and social context covered, albeit in a very superficial way. In terms of historiography, I'd suggest looking at Thomas Hennessey as a starting point (Northern Ireland: the Origins of the Northern Ireland Troubles and A History of Northern Ireland, 1920-1996) but also read as widely as possible. Hennessey is a respectable historian, but this is an intensely contested historiography, especially in Ireland.

Moving on: the 'Troubles' nomenclature covers a specific period from 1969 to the Good Friday Agreement in 1998. The immediate context for the Troubles is a social-political crisis in Northern Ireland: political dysfunction/corruption, widespread discrimination against Catholics and extraordinary police powers under the Special Powers Act. Northern Ireland had an active civil rights movement from the early 1960s, but it's riots between civil rights activists, the IRA and police in the summer of 1969 which started the process of escalating political violence which became 'the Troubles'.

British troops were deployed on the streets of Belfast in August 1969; in December 1969, a schism within the IRA led to the emergence of the Provisional IRA — the faction which advocated and carried out an armed struggle over the subsequent three decades. I'd look at Richard English's work on the history of the IRA — Armed Struggle - The History of the IRA is a good place to start. Again, caveats about reading widely apply.

The rest of the Troubles is a brutal cycle of violence between paramilitary groups, the security forces and state organs like the judiciary; attacks on civilians; political repression by the British government trying to keep the situation under some semblance of control; ceasefires being made and broken; negotiations and efforts at de-escalation taking place with varying degrees of success. Here's a nifty interactive chronology from The Guardian; you should also check out the work done by the CAIN project at the University of Ulster; and again, the point about reading as widely as possible applies here.

Long answer, but also insufficient in many ways — hope it helps to some degree, anyway.

The origins of the conflict are the centuries of British imperialism in Ireland, culminating in the Ulster Plantation of the 17th century, when land in Ulster was confiscated from Gaelic chiefs and given to Protestant settlers from England and Scotland to settle.

In the 19th century there was a long, hard struggle by Irish nationalists to achieve home rule for Ireland by democratic means, through the British parliament. When the Home Rule bill was finally about to be passed in 1914, Unionists in the north began to import arms, supported by sections of the British military, and in defiance of the democratic process.

Then came the 1916 Easter Rising in Dublin and a subsequent Irish civil war, which culminated in the partition of Ireland in 1922. The mainly Protestant unionists only had a majority in four counties in the north, but gerrymandering ensued in order that they might include as much territory as possible in the new province of Northern Ireland, which consisted of six counties.

Catholics in the north were systematically disenfranchised and discriminated against in employment, housing, voting, and other rights, and subjected to occasional acts of violence and police brutality, as well as triumphalist Orange parades through their neighbourhoods. From this situation a civil rights movement developed, and in response unionist paramilitary organisations like the UVF reformed, along with the resurgent provisional IRA.

It's a common misconception to think that the conflict was mainly a religious one, in fact, as the other commenter has pointed out, the sectarian divide was only a contributing factor, though a major one. The IRA, for instance, was a secular nationalist organisation, some of whose heroes, such as Wolfe Tone, were protestants, and whose activities were condemned by the Catholic hierarchy. Rather, the issues in the conflict were imperialism and nationalism, with the protestant/catholic divide being a rough but not absolute indicator of loyalties.