A user story is thus similar to a use case but "smaller". It's smaller in the sense that it should be possible to implement within a short period of time. The final product that you deliver to customers will be the result of implementing many such user stories.
"A user story is a very high-level definition of a requirement, containing just enough information so that the developers can produce a reasonable estimate of the effort to implement it. A good way to think about a user story is that it is a reminder to have a conversation with your customer (in XP project stakeholders are called customers) . . . . [U]ser stories are small, much smaller than use cases. In XP a user story must be able to be implemented by two people in a single iteration/cycle, therefore if you’re working in one week iterations each user story must describe less than one week worth of work."
Therein lies a challenge: along what lines to you divide the user stories so that they are each sufficiently small? I'll explore the alternatives in a future entry.