In the Middle Ages, kings and popes fought over who would appoint bishops because each side wanted power. The power to appoint bishops was an important power. Whoever had it would gain temporal, and not just spiritual, power. Therefore both the kings and the popes wanted to be the ones to appoint the bishops.
In the Middle Ages, bishops were powerful people. This was due in part to their religious authority. Since so many more people in those days believed that they had to do what the Catholic Church said, bishops could have a significant amount of influence over people’s actions. Kings and popes both wanted to control the bishops since the bishops could influence people. However, the more important fact about bishops was that they had wealth and the temporal power that went with it. The medieval church had a great deal of land and money. This meant that it also had a great deal of political power. Because bishops controlled large amounts of land and wealth in their localities, both the secular government and the Church wanted to control them.
Thus, the popes and the kings both wanted to be able to appoint bishops because that would allow them to have more control over the bishops. By controlling the bishops, they could increase the amount of power that they wielded.