A secure server (also called SSL server) generally refers to a web server that supports any of the major security protocols, like SSL / TLS that encrypt and decrypt messages to protect against third party tampering.
Online businesses and retailers in particular use secure servers to guarantee customers security when making purchases online as the payment or personal information can be translated into a secret code that’s difficult to crack. Major security protocols include SSL, SHTTP, PCT, and IPSec.
See the Server Types page in the Quick Reference section of Webopedia for a comparison of server types.