The Export Permission extension is designed to help restrict who has the ability to export records in your database.
It adds a new permission that allows the Export option to appear in the drop down Actions menu after a search.
When this extension is enbled, users that are not explicitly granted this permission do not see the Export option listed.
Please note, this extension does not technically prevent a user from exporting a CiviCRM database, it only removes that option from the Actions drop down list. Enterprising hackers can figure out ways to convince CiviCRM to provide the export. Additionally, any user that can view all Contacts can export the data one way or another - even if it means copy and pasting from each screen.
Additionally, if you don't want a user to have the export option, be sure to remove their permission to access CiviReports (since CiviReports provides a different path to exporting records).