A SSL certificate is a way to encrypt a site's information and create a more secure connection. Additionally, the certificate can show the virtual private erver's identification information to site visitors. Certificate Authorities can issue SSL certificates that verify the server's details while a self-signed certificate has no 3rd party corroboration.

And why it has been possible to exploit this: http://article.gmane.org/gmane.os.openbsd.misc/211963
xkcd: http://xkcd.com/1354/
history: http://www.smh.com.au/it-pro/security-it/heartbleed-disclosure-timeline-who-knew-what-and-when-20140414-zqurk.html

The Heartbleed Bug is a serious vulnerability in the popular OpenSSL cryptographic software library. This weakness allows stealing the information protected, under normal conditions, by the SSL/TLS encryption used to secure the Internet. SSL/TLS provides communication security and privacy over the Internet for applications such as web, email, instant messaging (IM) and some virtual private networks (VPNs).

Décrypter un fichier crypter par cle publique rsa avec cle privé
openssl rsautl -in fichier_chiffre -out fichier_clair -decrypt -inkey votre_cle_privee

et pour chiffré

openssl rsautl -in fichier_clair -out fichier_chiffre -encrypt \
-pubin -inkey cle_de_votre_ami