Go to the system designer and open the "Operation Permissions". Search for the "Export list records" operation and there you will be able to grant necessary access to people who need to export their data.
To enable all system users to export data from bpm'online, just go to operation permissions and find permission with code "CanExportGrid" and add "All employees" role there.
To access the import operation, the users/roles must have permission to perform the “Excel import” (CanImportFromExcel) system operation:
For that you need to go to Operation permissions section and find permission with code "CanImportFromExcel" and add the needed role there.