This question was asked a year ago, however the vast majority of the comments were deleted due to rules violations. I'm interested in learning more about the conflict and I would appreciate some expert insight. Thanks!
When the word Pakistan was first used, it was presented as Pakstan (minus the "i") in a pamphlet distributed by Chowdhary Rahmat Ali. It was, at that time, also an acronym that meant Punjab, Afghanistan, Kashmir, Sindh, Baluchistan. All Muslim majority areas in the Indian subcontinent, with the absence of East Bengal, which was to later become East Pakistan, and is now Bangladesh.
Fast forward to 1947, and India is partitioned on religious lines. The muslims go to Pakistans, the Hindus to the new Union of India. Both these domains had several kingdoms, who could choose between joining India, Pakistan, or remaining independent. The latter was basically no option, because neither India or Pakistan would allow domains to exist within their borders, and the UK which had been handling defense for these domains was not really interested in ensuring protection of these domains, hundreds of whom would otherwise choose to stay independent.
Kashmir happened to be ruled by a Hindu king, with a majority of Muslim population in the state. Now the king was inclined to join India, but he was not really willing to give up the wishes of the majority of the population. The situation was compounded by the fact that the Hindu majority are of Jammu, and the Buddhist majority Leh-Laddakh region would rather join India, than Pakistan.
In October 1947, the Pakistani army invaded Kashmir and kept up a steady advance. Raja Hari Singh asked India for assistance, and the Indian government offered it on the condition that he would sign accession to India.
Hari Singh signed the document, and Indian troops arrived by air to Srinagar, one of the important cities that was about to fall. They worked with the army of the kingdom, several areas were recaptured.
Eventually, the Prime Minister of India, Jawaharlal Nehru asked the UN to intervene and arranged a cease fire, against the wishes of his cabinet and the army. While he was at it, he also promised a plebiscite, which would hardly have a meaning without the approval of the cabinet.
In the words of General Manekshaw, one of the most celebrated generals of India, this was the demeanor of Nehru when the document of accession was handed to him:
As usual Nehru talked about the United Nations, Russia, Africa, God almighty, everybody, until Sardar Patel lost his temper. He said, 'Jawaharlal, do you want Kashmir, or do you want to give it away'.
Sardar Patel was the Home Minster of India, and was overseeing integration of princely states into India. He was also the popular choice to be the first Prime Minister, until he stepped down in favor of Nehru on request of Gandhi.
In any case, the position of the armies at the ceasefire of 1949 are what we call Line of Control in India. It is, for all practical considerations, the international border.
India and Pakistan both rejected formulas by the UN for mediation and plebiscite for a long time. In 1953, pro-Indians siezed power in Indian Kashmir and declared in support of India. In 1956, Nehru withdrew the offer of plebiscite claiming the Kashmiris had already declared support for India.
Wars have been fought, diplomacy engaged, but the situation of India and Pakistan's claim on the territory remains largely unchanged.