Diplomats from several countries met together at the 1954 Geneva Conference to discuss issues concerning the recently-lost Korean War and the rising conflict in Vietnam. Nothing was resolved about the Korean War, but the conference adopted the Geneva Accord concerning the situation in Vietnam.
Briefly, the Geneva Accord stipulated that Vietnam would be divided along the 17th parallel into North Vietnam and South Vietnam. Ho Ch Minh and the Viet Minh would rule a communist government in the North with the capital at Hanoi, and South Vietnam would have a non-communist government set up by the French with its capital in Saigon. The Viet Minh would withdraw from the South and the French from the North, and there would be prisoner exchanges. In 1956, elections would be held to create a unified government.
The United States refused to sign the accord but agreed to abide by its terms. However, the United States government was convinced that if elections were held, the communists would win and take over all of Vietnam. The United States was adamant about stopping the spread of communism. To achieve this, the United States did not comply with the Geneva Accord and instead took over (from the French) as the dominant foreign power propping up the anti-communist Vietnamese regime in South Vietnam. The United States began to pour more and more financial and military assistance into South Vietnam. This resulted in the disastrous Vietnam War, which didn't end until 1975. When it finally concluded, Vietnam became a unified nation, just as it presumably would have earlier if elections had been held in 1956.
In many ways, it was not the United States' decision not to uphold the elections promised by the Geneva Accords. Ngo Dinh Diem, the prime minister of the newly partitioned South Vietnam, refused to hold the elections, and the United States had already thrown its support behind Diem. Prime Minister Diem made the claim that elections would not be valid because the Communist North would never hold free and fair elections anyway. The Geneva Accords stipulated that elections would be held in 1956, but it did not set up any provisions for exactly how to hold them. South Vietnam had not signed the Geneva Accords anyway, so Diem said that his country was not bound to them.
The United States saw Diem as a convenient partner in keeping Communist influence out of the region. Foreign policy was more focused on containing Communism than upholding true post-colonial democracy. The United States had already supported Diem's rise to power. Therefore, the United States felt it necessary to continue to support Diem for the time being, even in the face of his underhanded power grab.
Furthermore, North Vietnam had already violated the terms of the Geneva Accords by not withdrawing all of the Viet Minh forces from South Vietnam, and it was building up its military forces along the border. As a result, the United States kept a large force of military personnel in Vietnam, contrary to the terms of the Accords.
The basic reason that the United States did not comply with the 1954 Geneva Accords was that they did not believe that their side would win the elections.
According to the terms of the Accords, the country of Vietnam was supposed to be reunited after elections. Both the North and the South would vote to see who would govern the whole, reunited country. However, the United States was worried about the likely outcome of the vote. They knew that Ho Chi Minh, the leader of the North, was very popular. They also knew that Ngo Dinh Diem and Bao Dai, the Southern leaders, were not popular. Because of this, they realized that the election would lead to a "bad" result. This caused them to ignore the Accords and simply allow the North and South to remain separate.