Martyrdom is the acceptance of death rather than the continuation of life under conditions that are at odds with one's beliefs. The word is commonly associated with those who die rather than renounce their religion, but there is no reason why the beliefs concerned must be religious. The original meaning of martyr is "witness", and the martyr bears witness to the unjust auhority who kills her. But the witness is even more central to the concept of martyrdom than this: martyrs are only martyrs to those who witness their death and understand it as an affirmation of transcendent truth or morality over the unjust and immoral authority. From the point of view of the authority itself, the martyr is not a martyr. One man's martyr is another man's common criminal.
The strength of the martyr derives from their ability to undermine the authority that kills them by competing with it for the sympathy of these witnesses. A dictator who kills a liberal dissident may understand his own act as strengthening the unity of the nation against this pest, but his explanation of the event has to compete with one which sees it as an unjust and unlawful taking of life which contradicts basic principles of justice. In the Christian conception, this principle is "thou shalt not kill"; in the liberal conception, it is the silencing of criticism through violence.
The martyr's affirmation of the principles for which he dies has a great capacity to impress; such is the attractiveness of his principles, that he is willing to completely forsake his life for them. We wonder if the dictator is so assured. Furthermore, the martyr's great strength is that there is no violence that the dictator can do to him that undermines his case: it only strengthens his case. And so, when the dictator nevertheless responds with violence where it is clear that violence can do no good, the bankruptcy of the dictator is all the clearer. He can only answer with violence, a fait accompli, because he has nothing left to say.
In the case of Christian martyrs, this commitment to principles that completely transcended secular authority was an urgent threat to that authority. The possibility of martyrdom may well have played a role in the separation of church and state and the evolution of religious tolerance. While we usually understand the separation of church and state as a means of protecting the state from the influence of the church, it also protects the state in a more fundamental sense: if the state attempts to affirm a particular religious truth and suppress others, it will generate martyrs who bear witness to its unjust authority. This, in turn, will take legitimacy away from the state and threaten its existence. This is equally true for secular beliefs as it is for religious: the more tolerant the state, the more just it appears to those who it exercises authority over, and the more likely it is to endure.