The silsila is the named chain of transmission of a Sufi order, and it functions as the guarantee that the method a disciple receives is authentic rather than invented.
An unbroken line
A silsila is the sequence of masters through which an order traces its teaching back from the living guide, master to master, to the founder and, through him, ordinarily to Ali or to Abu Bakr and so to the Prophet. The chain is not decorative genealogy: it is the warrant of authenticity, since the authority to initiate and to transmit the litany is held to pass down the line, and a guide without a valid silsila has nothing to confer. Reciting the chain is itself a devotional act in many orders.
Where the chains divide
The point at which a silsila runs back through Ali, as most do, or through Abu Bakr, as the Naqshbandi line does, is doctrinally significant and marks the orders off from one another. Because the whole authority of an order rests on the continuity of its chain, disputes over succession are disputes over the silsila, and the splitting of orders into sub-branches is recorded as the branching of the chain. The institution thus makes lineage the load-bearing element of Sufi authority, in the same way that ordination lineage is load-bearing in monastic Buddhism.