Martyrdom refers to being persecuted unto death for the sake of serving and witnessing to God. It is one of the highest honors precisely because it involves sacrificing your very life for a higher cause. This concept is important when thinking about the Atonement of Jesus, because it establishes the principle that God is pleased by faithful obedience, not by death itself. Nor does martyrdom in any way suggest God is upset with you or punishing you. Here are some verses to consider:
Brothers, became imitators of the churches that are in Judea. For you suffered the same things from your own countrymen as they did from the Jews, who killed both the Lord Jesus and the prophets. (1 Thess 2:14-15)
Paul is saying that Jesus was persecuted unto death, as were the prophets. And Christians are not to be shocked if they experience the same. This makes little sense within the Protestant view of the cross (Penal Substitution), since in that view Jesus was judicially punished, not persecuted unto death Penal Substitution is contrary to the character of persecuted/martyr, and it also makes no sense if Christians are expected to face a similar form of death.
Precious in the sight of the Lord is the death of his saints. (Psalm 116:15)
From oppression and violence he redeems their life, and precious is their blood in his sight. (Psalm 72:14)
Why is the death of saints a "precious" thing to God? This makes no sense within a Penal Substitution framework, since nobody aside from Jesus would be capable of this. But within the Catholic-Biblical understanding of atonement and sacrifice, the lesson here is plain: precious in God's sight is the act of offering up their life for his sake, particularly due to martyrdom.
and to Jesus, the mediator of a new covenant, and to the sprinkled blood that speaks a better word than the blood of Abel. (Heb 12:24)
Therefore I send you prophets and wise men and scribes, some of whom you will kill and crucify, and some you will flog in your synagogues and persecute from town to town, so that on you may come all the righteous blood shed on earth, from the blood of righteous Abel to the blood of Zechariah the son of Barachiah, whom you murdered between the sanctuary and the altar. (Matthew 23:34-35)
Why does the blood of Abel "speak" so eloquently to God? Because Abel gave up his life in service to God. Abel was not acting as a Penal Substitute, but rather as a witness (which is precisely what the term "martyr" means in Greek, and used in that way in places like Acts 22:20; Rev 2:13; 17:6). And since Jesus is being compared to Abel here, the comparison only works if their death/offerings were of the same kind. The term "righteous blood" can only refer to their deaths being unjust, and thus their merit before God comes from their martyrdom. One other interesting note is that in the Matthew 23:34 reference above, Jesus says that the Jews will end up killing and "crucifying" some of the prophets and apostles. This is strange if the whole point of Penal Substitution was that Jesus was crucified in our place, taking the punishment we deserved. You'd think this is the last thing Jesus would say, or that the Father would allow.
For another great example, consider my recent post on how this martyr theme factors into Romans 3:25 and Isaiah 53. In these verses and other posts I've done on Penal Substitution, I don't think Protestantism is honest enough with itself to see that their view of the Cross is quite simply wrong, and even twisted. But hopefully if we can get the word out we can change minds.