How does a WebSphere or any Application server clustering work in the case when a physical server is unavailable due to power failure or other reasons?
WebSphere's web server plugin component routes requests to WebSphere cluster Web Containers (within Application Server JVMs). If it has communication failures with a particular cluster member, it will mark that member down and start routing all requests to the remaining cluster members until the original is available again.
The details vary depending on whether you have a load-balancer in front of the web server(s), where the web server(s) are located (same or separate box), but that's the general idea.
Also, if you want users to retain their HttpSessions when a cluster member goes down, you'll have to enable some kind of Session persistence/replication. WebSphere allows either an in-memory replication of Session data between cluster members or a database-backed persistent store.
(Here's a blog post where I collected some observations from a presentation on how the WebSphere plugin works.)