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A simple, non-anthropologist's explanation is that the close family is the smallest and closest segment, and will generally stand with each other. That family is also a part of a larger segment of more distant cousins and their families, who will stand with each other when attacked by outsiders. They are then part of larger segments with the same characteristics. Basically, brothers will fight against cousins, unless outsiders come, and then they will join together, as expressed e.g. in the Bedouin saying: "Me and my brothers against my cousins, me and my cousins against the world." 
The ancient Hebrew nation (the Israelites) is one of the better-known examples, with biblical tradition denoting 12 tribes originating from one common ancestor (Jacob). The largest segmentary lineage society today is believed to be the Pashtun people of Afghanistan and Pakistan, with some 50 million members organized into a vast tribal structure. Arab tribal officials say that Bani Tamim, an Adnanite Arab tribe, has more than 42 million members, who all trace their lineage back to one man called Tamim.
a system in which complementary opposition and genealogical principles of unilineal descent are used by residential groups as a basis for political mobilization in the absence of centralized political leadership
- Barth, F. (1973). "Descent and marriage reconsidered". In Jack Goody (ed.). The Character of Kinship. pp. 3–19.