The conext sensitive help on the StartSSL website states:
Combined Server and Client Authentication support with SSL/TLS server certificates
This appears to be a feature related to requiring your users to have personal security certificates installed in their web browser. From http://webadmns.blogspot.com/:
If you enable client authentication, the server validates clients by checking for trusted certificate authority, Known as CA root certificates in the local key database. To enable client authentication, you need to use SSLClientAuth directive.
... The server requires a valid certificate from all clients and returns a 403 status code if no certificate is present.
A friend of mine started a company called CryoKey that lets you generate a personal certificate that gets installed in your web browser. This type of certificate would be the type used for both client and server authentication.