If your community is Closed (private) then the only people to whom you've given access will be able to register an account and join the community. If someone registers to join your community but has not been given access, they won't be able to log into the community.
If someone tries to register an account with your community and they haven't been given access permission, you (as a community administrator) will receive an email to tell you that someone has requested to join your community. You can then approve or deny their request to join the community.
To view requests to join your community:
1. Go to the User management area of the Crowd Management menu and open the Requests tab
2. When Requested is selected in the Show drop-down box, you will see a list of all of the people who have requested to join your community.
3. Click Invite to allow that person into your community or Decline to prevent them from accessing your community.
If you change the Show drop-down box to Denied you will see any requests that have been declined by either yourself or another administrator. If you want, you can allow someone who's previously been declined to log in: click invite to allow them to access your community.