The nature of the papacy is evident in the way the different Popes assert themselves, as all powerful, this is evident throughout the documents. The Papacy figured that since God ruled over everything and they were the closest entity to God, they were entitled to the most power next to God.
They exercised this thought in the Papal Election Decree of 1059, when they stated their independence from the Secular Authority. The church deemed it there right to name their leader, the Pope, going against the governing leader of the people who historically chose the Pope. The Decree against Lay Investiture is another example of the way the new era of Papal thought. This document states the opposition the church has for the old tradition of bishops and other clergymen being invested by secular leaders. Gregory VII, a reformist prohibited this practice. Both of those cases bring to light the nature of the Papacy; that they thought it was there right as the interpreter of God to have the power over themselves and all those who believe in God, even the secular authority, The “Holy” Roman Emperor.
This position overtime did not waver much. The two sides, secular authority and the Papacy disputed in January and February of 1076, with Henry sending a letter of accusations and insults, and then the Pope responding) with a gentle prayer (or defending himself with a clever rebuttal. In 1122 the two parties compromised, but Innocent III, perhaps the most powerful Pope of his time, reasserted the claims for Papal Authority in the late 12th and early 13th centuries.
I think the conflict can be described the same way some described the cold war, granted the feud between the Papacy and the Emperor wasn’t of that magnitude but the feud seems to have the same principles. The two biggest kids on the block are bound to argue and not agree on certain matters, or ideas and eventually maybe even clash. The secular authority of the high middle ages and the Papacy of the same time didn’t battle with the sword, but rather with the pen and maybe more importantly the opinions and ideas of the common Christian of the time, which both sides had enormous power over.