When you change your domain's name servers to CloudFlare name servers, you keep your current hosting provider and registrar; but this allows CloudFlare to become your DNS provider. CloudFlare is then able to route potentially malicious traffic away from your site before it reaches your server.
CloudFlare can be accessed in two ways: through cPanel (basic mode) or by visiting CloudFlare directly (advanced mode).
If You Signed Up via Your HostGator cPanel
If you signed up for CloudFlare through cPanel, you should not change your name servers.
If You Signed Up on CloudFlare's Website
If you signed up for CloudFlare directly, you must change your name servers to use CloudFlare. Once your name servers are changed, any changes you make in cPanel will have to be made to the zone file containing CloudFlare. Advanced mode is only recommended for advanced users who cannot make the redirections that basic mode demands. If you attempt to add a domain via advanced mode, you will not be able to add the domain via basic mode until you remove it from the CloudFlare dashboard.