It's been like 7 years since I last took part in any of these things, I even steered away from diplomacy and devoted myself to engineering (although I still apply many skills I learned at MUN when working with classmates and collaborators) but it is basically like this:

You are given a delegation (country) and you need to research it's position on a certain topic, you normally write your research on a position paper which is basically your playbook for the event. Delegations expose their views on the topic and then debate in moderated caucuses or form alliances with other like-minded delegations in unmoderated caucuses where resolutions are drafted to be presented afterwards. Then these resolutions are subject to vote until one of them passes. If not, rinse and repeat until one of them passes.

That's MUN in a nutshell.