There are many user roles concerned with the ability to export data from The Layer.
A user's roles can be amended from Settings - Users. Select the desired user, and open the Roles tab.
Export-related roles are found under the Data Export header.
The majority of these roles determine the ability to export data from specific types of browsing sessions, aka work stacks.
The Exporter role can be used to grant access to all of the other roles within the section, except for Export Widget Data, which must be enabled separately, if required.
Having a role enabled will activate an Export button as part of the interface for that stack or grid.
Exporting via Data Manager
Performing imports and exports with Data Manager requires the CRM Data Administrator role, found under the Security Level header. This role should be enabled sparingly, due to the impact that Data Manager imports may have.