To Voldemort the Dark Mark perhaps symbolized the history of Slytherin House, the ability to speak Parseltongue, and more darkly, the power to hunt down victims and kill them. Tom spoke to the basilisk, telling it to kill, and thus he murdered Myrtle Warren in the restroom, using her death to turn his diary into his first Horcrux.
As a young student, Tom Riddle discovered the entrance to the Chamber of the Secrets containing a giant statue of Slytherin from whose mouth the giant basilisk emerged ( CS17). While not definitively stated in canon, the Dark Mark seems to have been invented by Voldemort (or Tom Riddle) as an homage to his revered ancestor, Salazar Slytherin, one of the four founders of Hogwarts.