A stigma was the negative association people placed on certain conditions or statuses.
As of 2152, Pa'nar Syndrome carried a stigma on Vulcan. Were T'Pol to admit to having the disease, she might lose her commission. (ENT: "Stigma") By 2154, her admission inspired other Vulcans to come forward, removing the stigma from the disease. (ENT: "Daedalus")
In 2373, when Miles O'Brien questioned if anyone had ever suspected that a vastly intelligent Julian Bashir had undergone genetic engineering, Bashir reminded him that success carried no stigma. (DS9: "Doctor Bashir, I Presume")