There were significant political conflicts between the two sides. The Boers treated all blacks very badly and did not give basic human rights even to the blacks working for them. They made them pay taxes but could not vote. It was said to be through religious reasons that the Boers treated blacks so badly. This awful treatment infuriated the British, who had abolished slavery in all its colonies as well as at home in 1834. The Dutch wanted to keep its slaves. Europeans working in the Boer territories were also mistreated. These "Uitlanders" as they were known were key to the Boers' economic success, yet were still denied the vote.
The war occurred also because of strategic reasons. The British had already seized Swaziland, Bechuanaland and Basutoland, which more or less surrounded the Boers who feared that if the British took any more territory, they could be under siege, particularly if their route to the sea was blocked. The British wanted to control all of Southern Africa, not just small areas which were isolated - the Boers were their main opponents.
There were economic issues involved in the war. The Boers took control of the Transvaal and set up the Orange Free State. They found gold in the Transvaal and this area became very rich indeed. Later diamonds were found in this area as well, and there was argument between the British and Boers over in which nation's territory they lay.
Certain individuals had a major role in provoking the war. Cecil Rhodes was probably the most ambitious of Britain's leaders abroad. He was a real imperialist, and strove to expand the British Empire further, especially through his dream of a "Cape Colony to Cairo" railway. He was strongly anti-Boer, and his actions seemed to shape British policy back at home. Also highly influential was Sir Alfred Milner, who was the British High Commissioner and was also strongly anti-Boer. He was supposed to be a peacemaker, but it were the demands he placed on the Boers which sparked the war, and he ended up looking more like a warmonger.
Paul Kruger, President of the Transvaal and leader of the Boers, did not want to give in to the Uitlanders, since he feared he would lose his position if they were given the vote. It was he who had ordered the first attack against the British in 1881.