The United Nations General Assembly designates a number of "International Days" to mark important aspects of human life and history (the comprehensive list of all days celebrated by the United Nations and its Specialized Agencies is available here: International Days).
United Nations Specialized Agencies, including UNESCO, can also proclaim World Days. In this case, the proclamation of international days depends on their governing bodies and internal regulations only.
UNESCO thus celebrates UN International Days related to its fields of competence, in addition to the other World Days, proclaimed by the Organization's governing bodies or other institutions.
The list of official messages by the Director-General of UNESCO on the occasion of International Days with which UNESCO is associated is available here.