Summary: Compromising in holiness is far more dangerous than severe persecution of a congregation and individual Christian.
Verse 12 - Jesus introduces Himself as having a two-edged sword. The significance of that will be plainly understood later in this letter.
Verse 13 - Jesus first tells the congregation that He knows that one of the greatest challenges they must deal with is dwelling where they do - Pergamum - the location of Satan's throne.
Pergamum was the seat of Roman government in Asia. It was called 'the Rome of the East'. It played host to many false cults, the more prominent being those of Zeus, Dionysos, Asklepios (the serpent-god of healing which was referred to as 'saviour'), and - most importantly - Caesar worship. Pergamum boasted magnificient temples to the Caesars. Of all of the seven churches or congregations of Asia, Pergamum was the one most liable to clash with the Imperial cult.
Being the seat of the Roman government and Imperial Cult in Asia, it is said here that Pergamum was the throne of Satan. Satan inspired the Roman government to be a real 'adversary' to the Church and Cause of Christ. Just as the Jewish synagogue is described, in 2:9, as the synagogue of Satan because Satan had inspired the Jews to fight hard against the Church, so the seat of Roman government is called the throne of Satan because Imperial Rome had become a powerful 'adversary' of the Church.
This is especially true at the time of the writing of this Letter (AD 66), because Nero was on the throne. In AD 64, Nero had set the city of Rome on fire. The truth that Nero had set the fire leaked-out and the anger of Roman citizens exploded. Nero publicly denied his guilt and proclaimed that the Christians were the arsonists and that this was only one demonstration of how dangerous the Christians are to Society. Nero issued an edict that, throughout the Empire, all Christians who did not deny their Faith in Christ Jesus and perform sacrifices in keeping with the Imperial Cult should be executed.
During this Neronian persecution, the members of this congregation held fast the Name of Christ by proudly calling themselves Christians and did not deny the Faith or religion of Christ. One of the members of the Pergamum congregation who was actually arrested and did not comply with Nero's edict was Antipas. We know nothing more about Antipas except that he was Christ's "witness" and Christ's "faithful one."
The word the KJV renders 'martyr' should be rendered 'witness'. The Greek word used did not take-on the meaning of 'martyr' until the Third Century. Antipas acted as a witness, testifying to those in Pergamum the reality that Christ Jesus is the only Savior, the only King of kings and Lord of lords, and the ultimate Judge of Mankind.
He was Christ's 'faithful one' in that he remained a faithful witness even til the Roman authorities killed him for his Faith.
We do not face persecution, today, in the United States to the extent that the Pergamum Christians did. Yet, if we openly 'witness' for Christ in our daily lives, we will face resistence and maltreatment. 2 Timothy 3:12, "all who desire to live godly in Christ Jesus will suffer persecution." If we do not notice others treating us differently, in a negative way, as we interact with them...we need to seriously examine how diligently we are witnessing for Christ and what effort we are applying ourselves in living godly according to the demands of Scripture.