A martyr was someone who is willing to die for what they believe in, such as philosophical or religious beliefs. Their actions can also inspire others to do the same. One who was obsessed with the need to sacrifice themselves for others was said to have a martyr complex. (TOS: "The Immunity Syndrome")
Shortly before Ramsey's execution, Commander William T. Riker told the Elected One Beata that "the execution of Mister Ramsey and his followers may elevate them to the status of martyrs. Martyrs cannot be silenced." (TNG: "Angel One")
General Ardelon Tandro was known to the Klaestron people as a martyr but was in the process of betraying his forces to a rebel force when he was killed. (DS9: "Dax")
Jaro Essa ordered Krim and Colonel Day to be careful in capturing Li Nalas on Deep Space 9 in 2370, as he believed his death would make him a martyr and the Alliance for Global Unity would fail in their goals. (DS9: "The Siege")
After Rom and several other staff members of Quark's began a strike, Brunt was not willing to hurt Rom, as he did not want him to become a martyr. Instead, Brunt had Quark beaten up by a pair of Nausicaans. (DS9: "Bar Association")
While possessed by the Ilari Tieran, Kes told Ameron he could either be a martyr to his brother's cause or rule at her side. (VOY: "Warlord")
In 2374, the Dominion and the Orion Syndicate worked on a plan to make it appear an anti-Federation Klingon ambassador had been killed by Gowron's forces, thus making him a martyr and increase anti-Federation feeling in the Klingon Empire. (DS9: "Honor Among Thieves")
The script of the Star Trek: Deep Space Nine episode "The Reckoning" notes that the reason Kai Winn Adami stopped the Reckoning was that she saw "a martyr in the making – the last thing she wants is to spend the rest of her life standing in the shadow of a statue of Sisko". The script of "Profit and Loss" has Natima Lang reassuring her students, Rekelen and Hogue, that she has no intention of letting them become martyrs. Both scenes were cut.
Also that year, fearing he would die because of their actions, Jake Sisko referred to the crew of the USS Valiant, Nog included, as "a bunch of delusional fanatics looking for martyrdom. " (DS9: "Valiant")