Wikipedia - User story:
"When the time has come for creating user stories, one of the developers gets together with a customer representative. The customer is responsible for formulating the user stories. The developer may use a series of questions to get the customer going, such as asking if some particular functionality is desired, but must be careful not to dominate the idea creation process."
On extremeprogramming.org: "User Stories are written by the customers as things that the system needs to do for them. They are similar to usage scenarios, except that they are not limited to describing a user interface. They are in the format of about three sentences of text written by the customer in the customers terminology without techno-syntax."