You may want to check out Sessions in WebSphere - Getting Started.

Sessions provide affinity, so that requests from a certain browser are routed to a certain application server. For example, let's say you have two application servers in a cluster. When a browser requests an application from the cluster, either application server 1 or application server 2 will send the browser the application. If application server 1 is the application server to send the browser the application, subsequent requests from the browser will route to application server 1, and will not invole application server 2, until the session is destroyed.

Session affinity improves performance, by allowing sessions to be accessed from cache in the application server, instead of having requests bounce between different application servers in a cluster.

Session affinity can be verified by checking the application server SystemOut.log file. When session affinity has been estabished with application server 1, only application server 1 SystemOut.log file should contain events from the browser. 

~]# $was_home/profiles/<profile name>/servers/JVM1/logs/SystemOut.log
~]# $was_home/profiles/<profile name>/servers/JVM2/logs/SystemOut.log

Workload Management (WLM) is the brains behind affinity. WLM is how WebSphere determines if a request should route to application server 1 or application server 2. In fact, WLM has the knon how to send the first request to app server 1, the next new request to app server 2, and to then bounce requests back and forth between the application servers.