The iron triangle (in US politics) is a way of talking about the relationship between Congress, interest groups, and federal agencies. Congress is like the president and the people in the US who control laws and decisions. Interest groups are groups like the National Rifle Association and the American Medical Association. They are organizations that speak out on behalf of their members' interests. Federal agencies are like the Environmental Protection Agency and the National Park Service. These agencies are controlled by the government and they are responsible for enforcing federal laws and regulations.
The iron triangle occurs when Congress, interest groups, and federal agencies work together. For example, Congress might pass a law that affects how a particular industry works. This law could be in the interest of an interest group, like the American Medical Association, or in the interest of a federal agency, like the Environmental Protection Agency. This law will usually require a certain amount of money from the government to be spent. The interest group and federal agency could work together to make sure that it has enough funding to accomplish its goals. In this way, the interest group, federal agency, and Congress become connected in what is known as the iron triangle.