Charlemagne was a ruler in Christendom who had wished to improve the church and be crowned emperor by a pope. He protected struggling Pope Leo III and gained his loyalty. The pope eventually crowned him emperor.
I, Pope Leo III, pronounce you Emperor of Christendom.
Meanwhile, the Eastern European Church saw this as an insult, leading to a larger gap of ideas between the two. This also strengthened the Western European Church. This coronation would contribute to the Great Schism, or split between Catholic and the Orthodox Church.
Why has a Pope appointed a king? It is disgraceful.
While the Schism split the two Churches, the relationship between Pope and Emperor was not always peaceful. An example of this is when Pope Gregory VII claimed the rights to appoint bishops and dethrone kings. He also claimed to be superior to secular and non-secular leaders.
Roman Catholic Church
Our Pope has control over bishops.
Eastern Orthodox Church
Our bishops have the power.
The king, Henry IV, did not obey the claims and rules the pope had made. This lead him to be excommunicated from the church. He was cast out and sought forgiveness from the pope. Gregory had freed Henry's servants from their feudal oaths and pledges.
You do not disobey my rules. I excommunicate you from the Church!
He can't do this. He will pay for this.
Henry waited outside of the castle for three days until the pope would see him. Gregory forgave him, but Henry later stormed in with armed soldiers and forced him from office. This might have ended a generational quarrel, but the power balanced between Pope and king became an issue again.
He cannot keep me out here forever. Three days is far to long to not see someone.
To potentially solve this problem, the Concordat of Worms was established. It gave only the Pope the power to choose bishops, but a king could give grants of land to win a bishops loyalty. In turn, the Concordat was not a success and quarrels between Pope and king persisted for years to come.
The Pope gets the power to appoint bishops. Oh and lets use bribery to gain loyalty. This will solve all of our problems.