Composer permissions are based on the editor's admin user group.
Admin users can only be in one admin user group at a time, and the group they belong to will determine what that user can do on a particular page in Composer (see Moving an admin user to a different admin user group for more about admin users and groups).
Each admin user group has a default level of permissions assigned on the Permissions tab of Composer. For more information about global permissions, refer to Set Composer admin permissions.
In addition, each individual page in Composer has its own permissions settings. To navigate to Permissions, click on the pink gear (settings) icon in the lower right of any page, and then select Permissions on the pop-up window.
The Permissions tab displays a row for each admin user group that's been created on your site. Each group can be assigned a permission level using its corresponding dropdown menu.
Each permission level builds on the last. The rights attached to each level are explained in Define Composer permission levels.