The other churches would hear what Jesus had predicted concerning the ongoing persecution in Smyrna. Inevitably, such information would cause brotherly concern and personal fear that the same persecution might come to them as well. What application should they take from what had been said about Smyrna? The application was to realise that true believers would not be hurt by the second death.
What is the second death? Revelation 21:8 says that it is a description of eternal punishment. The first death is physical, and for some it comes through martyrdom. Others will experience it in other ways. Yet there is something common to all true believers and that is they shall never undergo the despair of a lost eternity. What is important ultimately is not how we succumb to the first death but whether or not we will experience the second death. Those who trust in Jesus and serve him with devotion will never be affected by the second death.
Jesus points out that the second death is painful. This is a reminder that a lost eternity is a conscious experience and we can say that it will be painful physically, intellectually and emotionally. Intellectually, those who suffer it will know that it will never end, so they will experience hopelessness. And who can estimate the effect of such despair on the feelings of those who endure it?
Why would Jesus remind the churches of this reality? One reason would be to remind the believers of the importance of personal gratitude to the God of salvation. Another reason would be to stress the urgency of evangelism, that those heading towards the second death would be warned about it. And a third would be to respond intelligently when they heard that the believers in Smyrna had suffered martyrdom, because although their deaths would bring sorrow they would not bring the despair linked to those who die the second death.