Which users have which of these quick link icons shown is controlled through a dashboard page at Dashboard > System&Settings > Basics > Toolbar Quick Links.
For users that do not have the Toolbar, have a look at the even more convenient Front End File Manager addon.
To add Toolbar Quick Links securely on a multi user site, you will also need to set up File Manager permissions at Dashboard > System > Permissions > Files.
You may also want to set up Advanced Permissions (though Advanced Permissions is not a prerequisite).
https://marketplace.concretecms.com/documentation/installation/installing_concrete5/
https://marketplace.concretecms.com/documentation/how-tos/designers/using-advanced-permissions/