"Saṃgha" refers to the organized group of ordained practitioners that centred on Sakyamuni and extended all over India. It can also refer to the individual cells of the Buddha's followers that were scattered around the country. We also use the expression "Sakyamuni's Saṃgha" to refer to it. In fact, it has been a question whether or not an overarching organization actually existed, but we feel we have been able to prove that it did. 

The Saṃgha was not a centralized organization like the Roman Catholic Church, but a lot looser, like a store in a franchise chain such as the convenience store Seven Eleven. Each store is basically independent, and responsible for its plot, equipment and fittings, as well as its loans, employees, stock and management, and for any profits or losses. However it pays a franchise fee, and buys in stock through Seven Eleven supply routes. It also profits from the group's know-how concerning stock variety, display and management. Each store is thus connected with others all over the country by the brand and its know-how.
Sakyamuni's Saṃgha was similarly organized. Each of the small Saṃghas scattered around India was independent of one other; they had the authority to confer ordination as well as to punish monks who offended against the regulations. Judgements, the independence or amalgamation of saṃgha, and the acquisition or dispersal of assets were all within their jurisdiction, based on the rules, procedures and ceremonies called karman. Even Sakyamuni himself could not dispute the results determined through the karman.
What melded the individual saṃghas together were the Buddha's teachings (Dhamma) and, in particular, the rules and regulations (Vinaya). A system of a single Vinaya for all saṃghas came into operation throughout the country. All ordained practitioners were obligated to attend the twice-monthly Posadha ceremonies and the annual Summer Retreat, and to adhere to the custom of wandering.
The history of the formation of Sakyamuni's Saṃgha throws light on the question of how and by what means this system came about, and of the nature of the role played in it by monks. Another question is how the Saṃgha incorporated the specific way of life of Buddhist practitioners, as opposed to that of those of other religions.
In order to understand Sakyamuni's life, we have to look at it in connection with the history of his Order. We can only do this through the way of life. This is simple enough if we merely list events, but it would be impossible to write an accurate biography of the Buddha unless we knew, for example, when we speak of his wandering life in Sāvatthī, the period of time during which wandering was possible, which routes he used, what means of transport were employed, how much distance could be covered in a day, and how many days were necessary to travel from one place to another.
For a detailed study of Sakyamuni's Saṃgha, please refer to Essay 14 in Monograph 13.