If Firefox can't access a secure site (one that starts with https) you will see an error page with the heading Secure Connection Failed and a message about the error.
When a website you visit attempts to secure communication between your computer and the website, Firefox cross-checks this attempt to ensure that the certificate and the method the website is using are actually secure.
Some websites try using out-dated (no longer secure) TLS mechanisms in an attempt to secure your connection. Firefox protects you by preventing navigation to such sites if there is a problem in securely establishing a connection. When this happens, you will see an error page with the option to report the error to Mozilla.
Firefox uses certificates on secure websites to ensure that your information is being sent to the intended recipient and can't be read by eavesdroppers. For a list of certificate warnings and error codes, see the article What does "Your connection is not secure" mean?.