You can have iCloud calendars, local calendars, or calendars subscribed froma CalDAV server.
As you can see, I have On My Mac (local), iCloud, Gmail, and the Birthdays calendar. Within iCloud, I have a subscribed calendar showing US Holidays. I explain how to get a new calendar, depending on how you are currently set up.
There are no other categories besides Subscriptions:
You can create a new calendar in the On My Mac section (ie a local calendar that exists solely on your Mac) by selecting New Calendar from the File menul and choose On My Mac as the type. If that is not available, see the next section.
iCloud and Subscription categories:
You can create a new Calendar in iCloud, but it is a little tricky to get a Calendar to show in On My Mac. Since you have the Birthdays calendar, select it, then right-click in the space below it and select New Calendar. That will make a new, untitled calendar On My Mac. From then, you can create new calendars within On My Mac from the File Menu.
If you don't have iCloud calendars and want them, you would need to turn on iCloud Calendars in the iCloud System Preferences. If you don't have multiple Macs and iDevices that you want all in sync, then you don't need to use iCloud. Even if you don't have multiple Macs and devices, you may still want it if you travel without your Mac. You can log into the iCloud web site on any computer and access your iCloud calendars, contacts, and email.