What was the political significance of the investiture conflict?

The investiture conflict was one very public aspect of a larger struggle for power. Precursors to it could be seen 300 years earlier at the coronation of Charlemagne by Pope Leo III. The larger questions were ones like:

Can the Pope tell a monarch what to do?

Should a monarch have complete control of what happens in his territory?

Is a king theocratic (ruling by the choice of God) or a human who happens to have power?

Should the church be involved with 'worldly' things like who is the ruler, how is a state organized?

Is the leadership of the church in the hands of the pope or the abbots of the wealthy monasteries?

How people chose to answer these questions had profound consequences for the development of Europe. Some possible answers:

Charlemagne, King of the Franks: "The Pope shouldn't tell me what to do. My father and I saved him from the Lombards. I am anointed by God like King David and I know what is best for my people."

Holy Roman Emperor Henry IV: "I should have the right to choose who is a bishop in my lands. Much of the church property in Saxony is held in vassalage to me. This right has been held by my predecessors for generations. For the last hundred years the papacy has been weak compared to the flourishing northern abbeys. What makes Pope Gregory think he can change the rules now?"

Pope Gregory VII (Hildebrand) with Cardinal Humbert: "I am the vicar of Christ on earth. The papal office is universal in authority can cannot err. I am the true successor to Constantine and my actions can only to be judged by God. I have in my hand both the temporal and spiritual swords. I may allow some of these kings or emperors to have authority for the good of the Christian mission, but if they misuse that power, I will reclaim it and give it to who I think deserves it. I will not tolerate simony (selling of offices) or lay investiture (letting laymen choose bishops). Only by submitting to my will, as the bishop of Rome, can anyone achieve salvation."

Abbot Hugh of Cluny: "We have had a balanced approach of the church growing from the support of these theocratic monarchs for hundreds of years. Piety in society is increasing and our monastic orders are thriving. Gregory, in pursuit of his own power, it upsetting a system that works well and does not need reformed."

Cardinal Peter Damiani: "To bring God's love into this world, the church must lead by example. Bishops must stop cohabiting with women and siring bastards. We must show the laity how to act by having a change within our hearts toward charity and an emotional connection with God. In this way we will elevate Christendom, not by locking horns with the emperor."

Pope Paschal II: "We have seen how difficult it was for Gregory to keep laymen out of church affairs. My simple solution is that we must divest ourselves of our lands and our riches, turning them over to the local rulers, and reconstitute ourselves as a purely spiritual organization. In exchange, the kings and emperors must stay out of our affairs and allow us to work freely in their lands. Our bishops must not be prosecuted under their courts as all churchmen are answerable only to me. In constructing this new arrangement, we are returning to the original apostolic poverty. We will spread the gospel, not as rich princes, but as poor itinerant preachers." [Note: this policy was abandoned because everyone hated it except Paschal and the German emperor.]

All that as a preface, your question asked what the political repercussions of this many-sided debate were.

1) The papacy reached the apex of their power from about 1073 to 1300. They could call for crusades, decide who was or was not a legal choice for a throne, tell kings what to do (with varying degrees of success), and collect huge amounts of money into their coffers. Arguably the high-water mark for this powerful papal style was the rule of Innocent III (1198-1216). Even after the schisms of the 1300's, papal power continued to play an huge role in European life for centuries.

2) The power of states had already begun to rise as rulers like Otto the Great of Germany and William the Conqueror beat back the great barons and consolidated power around their courts. In spite of the efforts of the Gregorian reformers, this increase in state power would continue under effective rulers like Henry II of England and Louis IX of France. After the turmoil of the Gregorian revolution though, successful kings came to rely on effective bureaucracies to build a secular state rather than emphasizing the older ideals of theocratic kingship and the personal charisma of the ruler. One place these states failed to consolidate was in Germany, in part because the system of electors kept power in the hands of the nobles, but also because of the damage done to the Holy Roman Emperor's power after the assault by Gregory VII. Later emperors like Fredrick Barbarossa and Fredrick II Hohenstaufen burnt up much of their energy fighting with the pope over control of Italy. One could even say that the late dates of the unifications of Italy and Germany (both in 1871) even have their roots in the Gregorian revolution. The power of the pope was one of the things that prevented those countries from charting the course that France, England, and Spain followed in centralizing around a monarchical state.

3) The emotional shifts that occurred during the Gregorian revolution bore fruit for years as well. Clerical celibacy came to be enforced more strictly. The new piety was taken up by St. Francis and organized by Innocent III into the order of Franciscan Friars (actually named Friars Minor). The older monasteries of the Clunaic style dropped in influence since they were seen as old-fashioned and not prepared to cope with the new piety of the masses.

In short, this time period is referred to as the "Gregorian revolution" because of the major shift in thinking and its long-reaching political and ideological effects.

References: I strongly recommend The Civilization of the Middle Ages by Norman F Cantor.