Usually, on a story multiple people works, say, a developer and a tester. Then why does a story has only 1 assignee? What is the solution?

[Anuradha]

Multiple assignee to a story.

[Nic Brough -Adaptavist-]

The assignee is the person currently working on the issue.  JIRA is very strong on having one person, as when you allow multiple assignees, you always get cases where someone thinks someone else is working on it, and your users simply don't know who to talk to about it.  The assignee is expected to change over time, depending on who is currently dealing with it.

However, having other people associated with an issue is a good thing.  Use a group picker or multi-user picker to involve people, or single user pickers for people for dedicated tasks.  Or break up the story into sub-tasks and assign them to different people.