Well, its kind of as the name suggests, it a model United Nations.
Basically each school chooses a country(or several depending on how many people can be in each delegation and how many want to go) then each delegation has people assigned to different committees.
The each person will be represent their country on a particular set of issues which research is needed to be able to debate the issues and so you set about finding out your country's position on issue.
Then you will go to the MUN event (many different places host them) and there it is as the UN works and you discuss each resolution proposed.
It is very fun, countries yesterday were forcibly removed from the committees yesterday for doing things they were meant to, other countries were calling on others to be evicted from the committee and others were declaring war on others. Another funny thing was that the Health committee decided to send all of the world's waste to the US as they have plenty of free room, hahaha.
I am aware that their is an international way of doing MUN and an American way, so might be different for you Americans.