Persistence – which can also be referred to as “affinity”, “server affinity”, or “server sticky” -- is the property that enables all requests from an individual client to be sent to the same server in a server farm. Persistence is not turned on by default, but it is an option configurable for each Virtual Service.
Without persistence, the LoadMaster will direct traffic according to the load balancing algorithm, such as round-robin, weighted round-robin, etc. like in the diagram above.
With persistence, the LoadMaster will direct new connections according to the load balancing algorithm, but returning connections will go to the same server, like in the diagram above.
For a description of the various Layer 7 persistence methods, refer to the following article: What are the Layer 7 Persistence Methods?