Since I cannot possibly word it better, I will provide an extract from the book:

The Iroquois League united five principal Indian nations—the Mohawk, Onondaga, Seneca, Oneida, and Cayuga. Each of these nations had a council composed of delegates called sachems who were elected by the tribes of that nation. The Seneca Nation elected eight sachems to its council, the Mohawk and Oneida nations each had councils of nine sachems, the Cayuga Nation had a council of ten, and the Onondaga Nation had a council of fourteen. Each of these nations governed its own territory, and its own council met to decide the issues of public policy for each one. But these councils exercised jurisdiction over the internal concerns of that one nation only; in this regard they exercised powers somewhat like the individual governments of the colonies.

In addition to the individual councils of each separate nation, the sachems formed a grand Council of the League in which all fifty sachems of the six nations sat together to discuss issues of common concern. The sachems represented their individual nations, but at the same time they represented the whole League of the Iroquois, thereby making the decisions of the council the law for all five nations. In this council each sachem had equal authority and privileges, with his power dependent on his oratorical power to persuade. The council met in the autumn of at least one year in five in a longhouse in the Onondaga Nation; if needed they could be called into session at other times as well. Their power extended to all matters of common concern among the member nations.

Source: “Indian Givers.” (Jack Weatherford)

In the same chapter Weatherford makes some more relevant interesting points:

• The League was founded sometime between 1000 CE and 1450 CE, by Hiawatha and Deganwidah under a constitution they called the Kaianerekowa or Great Law of Peace
• According to the Kaianerekowa the sachems were not chiefs (so it was not a position associated with war leadership) but lawmakers. If they had to go to war, they would have to leave the civil position. It was a common tradition in Indian tribes to have separate leaders for peace and war.
• A sachem could be impeached for improper behavior or if he lost the confidence of his electorate. (Here the author states that the women of his clan could impeach and expel him, and choose a new sachem. This implies that while sachems were men, the electorate was women, which I have no idea if it was always true). Upon election to Council a sachem would "lose" their name and be henceforth referred to by their title.
• Only one person was allowed to speak at a time during political meetings and no interruptions/yelling were allowed, the purpose of debate being to persuade and educate, not confront.
• The League was allowed to admit new members. The decimated and displaced Tuscaroras from North Carolina were admitted as the sixth nation in 1722, and more such groups were added later. The new groups were not lesser members.
• The League did not have a supreme leader, meaning consensus was vitally important.
• The Iroquois chief Canassatego was the first person to propose a federal model for the American colonies, speaking at an Indian-British assembly in Pennsylvania in July, 1744. His argument was to make it easier for the Indians to deal with different colonies, each with its own policy.
• Benjamin Franklin, when he was the official printer for the colony of Pennsylvania was responsible for the publication of the records of various Indian assemblies and treaty negotiations. Building on his now-famous curiosity he developed an expertise and interest in Indian matters and eventually was appointed Indian commissioner for the colony. He held this post in the 1750's and became quite familiar with the political structure of the League of the Iroquois (in particular). Speaking to the Albany Congress in 1754, Franklin would echo the original proposal of Canassatego, and calling on the delegates of the various English colonies to unite and emulate the Iroquois League.

In case it isn't obvious, "Indian" here means Native American. I use that term both for ease of reading and also because the author uses it too. No offense intended of course.