Permissions
If you're a Super User of your site, you can edit the Sticky Notes for Statamic content.
All other users will need explicit permission. Note that these users also must have the "Access the Control Panel" permission.
Statamic 6 New
The addon-generated permission was removed in the upgrade, and replaced with Statamic's core Addon Settings permissions.
Under the Addons section of the Permissions management you will find the permission for Sticky Notes for Statamic's addon settings.
Statamic 5
If you're using Roles for your users, only those with the "Manage Sticky Notes for Statamic" permission will be able to edit and update the Sticky Notes content.