Détente meant many different things to many different people, which is one of the reasons it ultimately failed. Before examining various conceptions of détente we should establish what it was not. Détente was not entente, a friendly understanding between political powers. Détente was a "relaxation of tensions" (the Russians used a word with a similar meaning), an attempt to set up a code of principles that would regulate competition between America and the Soviet Union. It was hoped that some areas could be removed from the sphere of competition altogether, and that violence could be eventually removed as a tool of policy.
1969 marked the point when Richard M. Nixon, arguably the century's greatest Presidential practioner of foreign policy1, called for a new era of co-operation with the Soviet Union. In 1971, the Soviets held their 24th Party Congress which adopted a peace program. The two sides had different reasons for adopting these courses of action, and hence goals that were ultimately irreconcilable.
On the American side, Nixon saw détente as a way of coping with the Soviet Union's rising military power and the emergence of a truly bipolar world system. As the Vietnam War came to an end, it seemed that large cuts in the defence budget were inevitable (usually after wars the defence budget stays above the pre-war level rather than returning to below). Meanwhile, the Soviet Union's autocratic political system had no trouble seeking the military strength it so desired. America was faced with a situation where it was no longer the unrivalled military superpower.
In such a situation, it was hence natural that the USA would want to try and discourage the use of force as a tool of policy. If it was going to be impossible to persuade the American people and the Congress to massively augment the defence budget, then alternative ways would have to be found to pressure the Soviet Union and to stop it carrying out its goal of world revolution.
Nixon here was taking a particular view of diplomacy, which stood in sharp contrast to how Ronald Reagan saw the matter. Nixon's view holds that it is best to have contact with hostile states so as to be better able to offer them carrots and beat them with sticks. If the Soviet Union could be integrated into the world system (say, by making them reliant on foreign grain) then it would be in no position to upset the status quo by fostering revolution in the Third World and threatening the United States. Such a view accepted the continued indefinite existence of the Soviet Union, a proposition that at the time was widely believable.
Another part of détente from both the American and Soviet point of view was the need to control the strategic arms race. This was the purpose of SALT, the Strategic Arms Limitation Treaty. The Americans and Soviets were capable of destroying mankind between them, an eventuality which would hardly benefit world revolution nor pluralistic political systems. Avoiding a nuclear war was the primary foreign policy goal of both powers, however Khrushchev may have behaved in the Cuban Missile Crisis. Hence co-operation on stopping the arms race was valuable to both.
Yet beyond this one basic issue the Soviets had a very different conception of détente. The Soviets were nothing if not hubristic, and they partially agreed with the United States in seeing détente as a way of managing the transition of the United States into a world where the Western bloc was no longer dominant. However, they naturally had no intention to put up with the status quo - as the rising power, why would they? They saw détente as a way to manage relations with the United States to avoid catastrophic military conflict while the world revolution was busy coming about.
In official Soviet doctrine, it had long been accepted that you could not export revolution merely by military action. Revolution happened when internal societal conditions were ripe, and it was then the job of the Soviet state to support the indigenous revolutionaries against the capitalist-imperialist powers. The new era of Soviet military parity with the West was the first of true security for the Soviet bloc, and this power could be used to support world socialism without a threat to the socialist homeland.
The Soviet Union wanted to transfer its military parity into political parity, being able to act on the global stage according to the same rules that the United States did. That up until now they could not do this was to them demonstrated by the Cuban Missile Crisis. American nuclear missiles had been in Europe for some time, but as soon as the Soviets tried to base nuclear weapons in the Western hemisphere the Americans went ballistic. To them this was a double standard which military power would help them avoid in the future.
So the Soviets never saw détente as a way to uphold the status quo, but rather as a means of actually gaining more prestige and influence in the world. It would allow them to carry on the class struggle without the threat of nuclear armageddon or military crisis. A rise in tension would be ascribed to the US interfering in the Third World. So when the Americans and Soviets both picked a side in the Angolan Civil War in 1974 - 6 and Cuban regulars appeared to assist the Soviet side, the Russians did not see this as a violation of détente. The violation came from America's attempt to stop the spread of socialism by force of arms.
Détente sank after these misunderstandings became evident. It was essentially over by 1976, to be replaced a year later by Carter's impotency. At the height of détente Gerald Ford had been able to declare the Cold War over, but the Soviet Union's invasion of Afghanistan in 1979 soon kick-started it again. Although the idea of relaxed tensions had sounded good to Americans when it was a theoretical idea, when concrete deals were reached they were usually jumped all over by partisans on both sides. Liberals and conservatives alike complained the Soviet Union was taking Uncle Sam to the cleaners, and détente collapsed over a decade before the Soviet Union itself made an ungraceful exit from the world-historical stage.
1. Kissinger once assured Nixon that history would forget Watergate and remember his impressive foreign policy achievements. This may one day be true. The Soviets were themselves baffled by Watergate and the apparently inconsequential nature of Nixon's offences, and in their confusion they decided it was a conspiracy by hard-line opponents of détente.