When a terrible threat rises, Guardians look to the Vanguard, the closest thing they have to a command structure. These elite veterans coordinate the reports of roaming Hunters, the analyses of cloistered Warlocks, and the instincts of grizzled Titans into a single plan of action. And when Guardians fight as part of that plan, the Vanguard rewards them.
Vanguard Marks are tokens of favor that earn a trusted Guardian access to the Tower's armories. Listen carefully to the rumblings of Lord Shaxx, and you might come to believe that this system was meant to keep vital warfighting supplies from being wasted in the Crucible. Talk to Commander Zavala, and he will reassure you that the Vanguard Mark system exists for one reason: to get the best equipment into the hands of those who get the best results.
Guardians eager to win Vanguard Marks would do well to participate in Strike missions organized by the Vanguard.