The node.js cluster modules is used with node.js any time you want to spread out the request processing across multiple node.js processes. This is most often used when you wish to increase your ability to handle more requests/second and you have multiple CPU cores in your server. By default, a single instance of node.js will not fully utilize multiple cores because the core Javascript you run in your server is single threaded (uses one core). Node.js itself does use threads for some things internally, but that's still unlikely to fully utilize a mult-core system. Setting up a clustered node.js process for each CPU core will allow you to better maximize the available compute resources.
Clustering also provides you with some additional fault tolerance. If one cluster process goes down, you can still have other live clusters serving requests while the disabled cluster restarts.
The cluster module for node.js has a couple different scheduling algorithms - the round robin you mention is one. You can read more about that here: Cluster Round-Robin Load Balancing.
Because each cluster is a separate process, there is no automatic shared data among the different cluster processes. As such, clustering is simplest to implement either where there is no shared data or where the shared data is already in a place that it can be accessed by multiple processes (such as in a database).
Keep in mind that a single node.js process (if written to properly use async I/O and not heavily compute bound) can server many requests itself at once. Clustering is when you want to expand scalability beyond what one instance can deliver.
