Peace is the time period in which nations are not considered to be enemies or allies. Generally, foreign buildings military units will still suffer attrition if they are within a territory of a nation during peace. However, unlike nations at war, attrition is increased 200%.
In Diplomacy, nations will began in peace without having any rivaling or friendly nations but they can forge alliances and wage war. If a nation has decided to cancel an alliance, the nations involved with that alliance will be transferred into peace. This is to prevent a nation in suddenly declaring war on an ally, especially when the caller has military units in an allied nation's territory.
In the Diplomacy option, the icon for peace is a dove.