In a high availability cluster, what are "instances"?

Instances are Java EE server processes to which Java EE applications can be deployed and served from. In a clustered environment, a number of instances are created to help distribute the load of incoming requests (assuming these are fronted by a load balancer or an IP sprayer) and to build redundancy for continued availability of service without interruption due to failure/crash of one or more instances in the cluster. In other words, a cluster of instances prevents a single point of failure in the software layer of your topology.

Going a step further, session state replication provides continued availability of both service and session data so that site's customers can be agnostic to failures of software processes/hardware.