The main example of a détente was during the Cold War. In the 1970's, the United States and the Soviet Union improved relations. Both signed several treaties which made less amount of nuclear weapons each country had. During this time period, as China began to dislike the Soviet Union, the United States tried to make friends with China, giving the Soviet Union a disadvantage during the Cold War. This was often called “playing the China card.”
Détente primarily was concerned with relation between USA and USSR but other countries like China, West Germany and most of the European states also played their role in developing it. Their motives were mixed. The US proposed this because they did not want to have to go to war with USSR which would lead to all out nuclear warfare.
The literal and original use of the word, meant to undo a crossbow, the detention of the cord that launched the arrow. Which is why this old word was so appropriate in the above description.