Project permissions are created within Permission Schemes, which are then assigned to specific projects. Project permissions can be granted to individual users, groups, project/issue roles, or even anonymous users.
For a thorough overview of JIRA project permissions, management, and schemes, please see Atlassian's documentation.
Permissions Required for Common Actions
Permissions Required to Perform Action
|Modify the rank of issues in the backlog||Schedule Issues|
|Add/drag issues into sprints||Schedule Issues AND Edit Issues|
|Create sprints||Project Administrator|