Peacekeeping (at least in the sense of trying to stop conflicts that are actually going on) is one of the lesser parts of what the UN does. In addition to peacekeeping, the UN tries to help various countries develop economically via such things as the UN Development Program. It tries to enforce international law, as can be seen in the link below on the subject of the Rwandan genocide. They try to promote the general welfare of the countries of the world through organizations such as the World Health Organization (WHO) and the UN Children's Fund (UNICEF). The WHO, for example, was heavily involved in trying to prevent the spread of the SARS vaccine that broke out in Asia in 2003.
So, the UN's mission is not limited to trying to end conflicts that are actually going on. Instead, it tries to help prevent problems such as poverty and epidemics that might possibly lead to conflicts or other international problems.