In the letter to the fourth church, Jesus reminds them that he is the final arbiter of all things. He can see deep into the hearts of people. He can test motives, ignorance and intentions. He can them proclaim judgment with total fairness and justice.
Jesus commends them for the practice, faithfulness and growth in many different and important areas:love, faith, service and perseverance.
But like the third church, they are allowing people who are not following Jesus to have influence among them. In particular, he identifies a woman, who he calls "Jezebel." Jezebel was a queen in Israel, who introduced practices to the people of Israel that honored other gods, and pulled them away from the one and true God. And this "Jezebel" was doing the same thing.
She proclaimed to everyone that she is a prophet, taking a position of authority, of one who speaks for God. And using this postion, she has encouraged practices that dishonor God.
God will challenge her to repent. But if she does not, she and any who follow her will be judged.
For those who are not following her, they should persevere and be faithful in what they know is right and how to do. To those who persevere, he will give them a position and authority like that which the Father gave to Jesus. They will see hearts, motives and intentions. They will judge with complete fairness and justice.
It also says he will give them the "morning star." There is a lot of confusion of what this could be a symbol of. Some say it is Jesus himself. He is identified as the "morning star" in other parts of Scripture. So, this could refer to a new, vital relationship with Jesus. Some say it refers to the actual morning star, and acts as an indicator that a new day is coming. So, it could refer to the person witnessing the restoration of God's kingdom. Or both.
If I had to make a decision right now, I would have to say it is the first, because Scripture calls Jesus the "Morning Star," so the promise is for a new relationship with Jesus.