There are multiple scenario where restore is helpful
In case you bought a subscription from say iPhone but the subscription is not visible on Apple TV, clicking on Restore button from My Account or My Purchase will enable subscription on the Apple TV.
You have received subscription purchase confirmation from iTunes/Apple Store, but the subscription is still not active? Click on the Restore button from My Account or My Purchase and your subscription will be restored.
You have deleted and reinstalled the app or restores the device from a backup? Simply click on Restore button from My account or My purchase and your subscription will be enabled.