A user story is an informal, general explanation of a software feature written from the perspective of the end user or customer. The purpose of a user story is to articulate how a piece of work will deliver a particular value back to the customer.

When should we use user stories?

User stories help to achieve cross-team clarity on what to build, for whom, why, and when. Since they are easy to define, understand, and revise, they can become the standard way to communicate and summarize the functionality of the product by both technical and non-technical members.

When a user story is done?

Second, user story is done when it is ACCEPTED by PO. PO reviews a story for acceptance as soon as team marks it as COMPLETE. If the PO doesn't accept the story then the team would likely add more tasks. And yes you are right team should complete the story as per the scope agreed during spritn planning.