Observance of the Day began in 1982, following the 1981 UN General Assembly Resolution (A/RES/36/67) which reaffirmed that "since wars begin in the minds of men, it is in the minds of men that the defence of peace must be constructed" and declared the third Tuesday of September, the opening day of the regular session of the General Assembly each year, "shall be officially dedicated and observed as the International Day of Peace and shall be devoted to commemorating and strengthening the ideals of peace both within and among all nations and peoples".
In 2001, a further General Assembly Resolution (A/RES/55/2820) proclaimed that from 2002, the Day would in future be observed on 21 September each year; and in addition to the original purpose, declared that henceforth the International Day of Peace would also "be observed as a day of global ceasefire and non-violence, an invitation to all nations and people to honour a cessation of hostilities for the duration of the Day".
The International Day of Peace is marked each year at the UN Headquarters in New York by a ceremony near the Peace Bell. At 10am (local time, 2pm GMT, 2am on 22 September here), the UN Secretary-General delivers a message for peace, then rings the bell and calls on people throughout the world to reflect for a moment on the universal goal of peace. Following a moment of silence, the President of the Security Council makes a statement on behalf of Council members.
Peace and community groups around the world mark the Day in a number of different ways - more information about the Day, and what is happening around the world, is available on the International Day of Peace site, information particularly useful for students is on the UN CyberSchoolBus site, and the UN Department of Information fact sheet about the Day is available here.