Network Approval is a Hamachi Premium feature that allows you to require an approval process before new members are allowed to join a network you enable it for.
To enable it, simply right click the Network name, and go to Details...
Then go to Access and enable Manual Approval.
Your network will now require approval from the owner, or optionally any administrators you've configured for that network, prior to a user being granted access.
When a user requests access by attempting to join the network with its name and password, they are given the option to request access.
After the request is submitted, owners and configured administrators will see a flashing indicator next to the pending peer in the network list.
The owner/admin can then right click the request, and choose to Accept, Reject, or Reject and Ban the user of the request.