Jesus gives two promises to the overcomers. One is authority over the nations. The authority is similar to that which was given to Jesus by the Father. It is an authority to implement punishment as we can see from its description as being like a rod of iron that crushes pots in pieces. I would say that this is a promise connected to the dignity that believers will have on the Day of Judgement. Paul mentions in 1 Corinthians 6 that Christians will judge angels and the world. In some way, they are going to be involved in the process when Jesus judges the enemies of his kingdom.
The second promise is connected to the morning star. I would suggest that there are two ways to consider this. First, later in the book Jesus says that he is the bright and morning star (22:16), so he could be promising to the believers in Thyatira that they will have Jesus with them and for them for ever.
Second, the morning star is the star that is visible just before sunrise, or just before the day dawns. So here Jesus is informing his followers that they will see the arrival of the eternal day after the long dark night of sin. So in this promise, Jesus reminds his people what they will get (himself) and when they will receive the blessing (at the start of the eternal day).