I 'need to read either the Seam reference documentation or Seam in Action.
The conversation is a slice of the HTTP Session dedicated to a single browser viewport (tab or window). It maps one-to-one with a use case involving a single user, where the boundaries are something you decide based on the business logic. Those boundaries can be set various ways, either declaratively (XML) or programmatically (Java/Groovy/EL). The main purpose of the conversation is to extend the persistence context across more than one request to avoid detached entities. You also have the option of binding the conversation to a stateful pageflow, which makes the boundaries more well defined and constrains the user on a predetermined navigation path.
The business process is a persistent context (i.e., stored in a database) and therefore can stretch across any number of requests, sessions, or even application restarts. It maps one-to-one with a use case involving one or more users. The boundaries are controlled by a business execution language. Seam relies on jBPM to drive the business process described in jPDL. In some regards the business process is a multi-user conversation, though each task in the business process can itself be a single-user conversation. You can start to see how these two contexts build on one another.
If you want to learn about the business process in depth, and see more references to its relationship to the conversation, you can read the Business processes chapter of Seam in Action for free online.
http://manning.com/dallen