Caesaropapism is related to the power of the Byzantine emperor because it increased that power. Caesaropapism is the idea that the head of a country (in this case, the Byzantine emperor) should also be the head of that country’s religion. This idea is most closely connected with the Byzantine Empire. In that empire, the emperor was also the head of the Orthodox Church. He had the power, for example, to appoint the Patriarchs of the church. This increased the power of the emperor because he had control of the spiritual institutions of the empire, not just the secular ones. He could use his power to make sure that the teachings of the church would not undermine him in any way. He could also use his control over the church to appoint people to high positions. This gave him political power because it would allow him to have more ways to reward supporters by putting them in positions of power.
Thus, caesaropapism was an idea that increased the power of the Byzantine emperors. It gave them control over the church, which helped them have secular power as well. It also gave them an aura of divinity because they were also seen as the head of the church. This further legitimated their power.