An IGO (sometimes called an "Intergovernmental Organization") is an organization that is created by states (instead of by private individuals like an NGO is) for a specific reason. IGOs tend to be made to combat problems that are important to the states that create them.
One major IGO is the North Atlantic Treaty Organization (NATO). NATO was created by the US and by countries of Western Europe during the Cold War. It was an IGO because it was created by these states but was not part of the government of any one of them -- it was its own, relatively independent organization. NATO's purpose was to deter the Soviet Union and to otherwise increase the security of Western Europe and the US.
The World Trade Organization (WTO) is another important IGO. It was set up by various states to regulate trade among them. It is meant to reduce the likelihood of trade disputes and to, thereby, increase world prosperity.
IGOs are important to IR theorists because they increase the amount of contact between countries and (to liberals) decrease the likelihood of conflict between countries.