The United Nations has proved to be the major player in upkeeping of Peace and facilitating harmony between nations. It was formed as a result of worldwide conscious to part ways with war and destruction caused thereby and to create a new world in which all can survive peacefully.
The United Nations has organized several international conventions regarding every aspect whether the weapon, nuclear weapons, environmental conservation, discrimination, equal Status etc and it creates obligation over member states. The member states fulfill their duty to prove themselves in the Global Community and thus contributing to the Greater Good.
In the absence of the UN, this would rather not possible, beach and every nation will become independent without obligation toward each other and nations having potential aggression will rage war upon other states. There will be no forum to bring trivial disputes among nations and no such channel to resolve the dispute will result in war.
The major and superpowers will devour the smaller nation states and threaten their sovereignty. In a nutshell, the world would go back to anarchy which will ultimately increase the outbreak of third world war.