Index Server is heart of SAP HANA system and is responsible for processing all SQL statements sent to HANA database. This server contains SQL/MDX Processing engine that is responsible to process and analyze data in HANA db.
Index Server also contains Persistence layer for scalability and restoration of the system. In case of system failure, power failure or database corruption, Persistence layer is responsible for the restoration of HANA system to last save point.
When you are running complex and large calculations, and there is a system failure Persistence layer is used to ensure that transactions are either fully executed or complete undone using Session/Transaction Manager.
Session and Transaction Manager is responsible to keep track of statements that are executed in HANA system.