That's a pretty broad question, as /u/ChuckRagansBeard has already pointed out. There's a lot in here, from the late medieval history of Ireland where you have a fragmented island inhabited by the native Irish and the 'Old English' who existed in various states of loyalty or disloyalty to the Crown, and successive attempts by Henry VIII and his successors to consolidate their power. Elizabeth I was most thorough and insistent, crushing Catholic rebels in Ireland backed by the Papal States during the Desmond Rebellions and instituting a system of plantation whereby loyal Protestant settlers would be brought in the take over the land seized from those attainted.

The situation in Northern Ireland can be traced in part back to the Nine Years War, where Hugh O'Neill, earl of Tyrone, rose up against Elizabeth from his bases in Ulster, Ireland's most thoroughly Gaelic province. After some resounding victories exacerbated by state muddling, O'Neill was finally defeated after his attempt at an island-wide rebellion supported by Spain was crushed in the far south at Kinsale in 1601-2. O'Neill had been hoping to united with the Catholic Old English against the Crown, but this failed and he was forced to surrender some years after.

O'Neill was able to negotiate terms to retain his land and titles, but chose to go into temporary exile in the hope of returning with Spanish reinforcements. The new king, James I had been brought up a Protestant, and despite Irish hopes that a Scottish king would be sympathetic to their plight, James seized the lands abandoned by the O'Neills and their followers, setting up a plantation of Protestant English and Lowland Scots in Ulster to pacify to the Catholic, Gaelic population. This was nearly reversed during the 1641 rebellion and the ensuing Confederate Wars, but that's another story.

Stephen Ellis, The Making of the British Isles: The State of Britain and Ireland 1450-1660 (2007) is a pretty comprehensive overview.

If you're interested in hearing more about the Old English of Ireland: Aidan Clarke, The Old English in Ireland, 1625-42 (1966).

This is an incredibly broad and imprecise question so it is difficult to really form an answer. What precisely do you mean by "divided"? Why Northern Ireland is about 50/50 and the Republic is closer to 85/15? Why there has been a history of sectarian violence? Or just, to put it simply, why the violence throughout Irish history seems to fit Catholics vs Protestants?

These are all very different questions and the Irish Historians on this sub can all give great answers (they definitely can, I hope I can as well) but this is question is far too broad to tackle.

Very broad question but i'll do my best to explain what i know. A clear divide between the Protestants & Catholics would have taken place socially around the times of the Penal Laws following the Williamite Wars circa. 1690's, battle of the Boyne, siege of Derry, Enniskillen etc.