Content Type permissions can be inherited from the system host*, individual Sites, or permissioned individually. If you are hosting a single Site that all have the same administrators, then Content Type permissions might be more easily managed by editing the Content Type and using the permissions tab to distribute Content Type role/user access. However, a multiple-site implementation with various Sites that all need to be permissioned to differing roles/users will more easily be managed by setting up inheritance at the System Host/Site Level using Role Permissions.
To view the permissions set on a Content Type, mouse over the Content Types Tab and click on > Content Types. Then click on the correct Content Type title or click the pencil icon to edit the Content Type. Now click on the Permissions tab next to the Content Type Properties tab.
Content Type Permission Inheritance from System Host
Below is an image of a Content Type that is inheriting all its permissions from the "System Host". This means that permissions on this Content Type is inheriting permissions directly from the Role permissons themselves set at the System Host* level.
Setting Individual Permissions
While editing a Content Type, clicking on the Permissions tab and the "Permission Individually" button will stop any role inheritance coming from higher up the permission hierarchy and allows for permissions to be set on the Content Type itself.
*For more information on setting permissions on dotCMS objects from the System Host, please see the documentation on Role Permissions.