Under the pressure of the barbarian (non-Roman) peoples, the Western Roman Empire collapses and the last emperor is overthrown in 476. Western Europe is now divided into many kingdoms despite an attempt of reunification made by the Eastern Roman Emperor, Justinian (r. 527-565).
The Western possessions of the Byzantine Empire, a continuation of the Roman Empire, were limited to a region in central Italy, with Rome and Ravenna. Given this state of affairs, Gregory I the Great, Bishop of Rome (i.e., the Pope) from 590 to 604, developed diplomatic relations with the Western kingdoms. His successors undertook further initiatives, this at the gradual exclusion of Constantinople. In particular, they developed their alliance with the Franks. One of the most famous forgeries in history, the Donation of Constantine, composed around 760, was invoked regularly by the papacy in justification of its territorial claims in central Italy against the secular aristocracy. In this respect, it was at the origin of the Papal States. Some popes participated in the recurring revival of the Holy Roman imperial idea. First with Charlemagne (reign 768-814), whom Pope Leo III (r. 795-816) crowned emperor in 800, and who presented himself as the ruler of all the Churches. The Carolingian Empire ended in 924, and the imperial idea was reborn again with Otto I (r. 936-973), King of Germany, when he was crowned emperor in 962 by Pope John XII (r. 955-964), but this new Empire is mostly a German-Italian Empire. However, papal ambitions were limited; papal bulls were not widely disseminated. Moreover, the papacy passed into the hands of the Roman aristocracy, the election of the Pope being dependent on the people and the clergy of Rome.
The 11th century was a turning point for the papacy. With the intervention of the German Emperor Henry III (r. 1046-1056), who imposed Pope Leo IX (r. 1049-1054), the papacy was henceforth freed from the grip of Roman factions. Leo IX began a reform of the Church, which developed into the "Gregorian reform", named after its largest proponent, Gregory VII, Pope from 1073 to 1085.
The desire for reform began earlier, however, when it developed with the monks near the year 1000, namely to keep monasteries out of the hands of secular aristocracy (who had overtaken most monasteries during the post Carolingian decline in power, when central authority broke down). The movement started when the Abbey of Cluny was founded in 910 by the Duke of Aquitaine William III, who placed the monastery under the direct authority of the Pope. Cluny became a center of reform and the Cluniac order came into means rapidly, attracting many members of the aristocracy, as well as donations. In 1115, Robert of Molesme responded by founding the Citeaux Abbey, in order to follow more closely the Rule of Benedict of Nursia for monastic life, which he claimed had been perverted by the Cluniacs, advocating collective austerity instead. The new Cistercian order multiplied quickly, and more monasteries were built, like Clairvaux, founded by Bernard (1090 / 1091-1153), who became its abbot until his death. and perfection of the early Church, the Apostolic Church. It led to the founding of other monasteries, such as Fontevraud Abbey in 1101, and to new religious orders. Among the most important were the Mendicant orders, which included the Order of the Friar Minors (humble), founded by Francis of Assisi (1181-1226) and that of the Friar Preachers, founded by Dominic (1170-1221). Both had an innovative approach, well received at the time: they advocated [working in poverty and living on charity]; [without a permanent attachment to monasteries], the friars were [mobile, regularly travelling] to preach to Christians (in the cities) and “infidels." The Order of Preachers eventually aided the papacy in its struggle against dissident movements. Indeed, the impetus for reform occasionally led to more radical positions, with some movements setting themselves apart from the institutional Church. This was especially true of the "Good Men" and the "Poor Men of Lyon", respectively referred to by the Church (derogatively) as the "Cathars" (the Pure, or religious puritans) and the "Waldensians" (after Peter Waldo, founder of the movement). Such movements created religious and social instability; they were condemned by the Church as heretical, and were violently repressed (crusades, arrests and convictions).
The Gregorian reform itself concerned the secular clergy. The reform began with the papacy itself. Under Pope Nicolas II (r. 1059-1061), the rules of succession changed with the creation of a College of Cardinals in 1059, which was charged with electing the Pope (who thus escaped the influence of Roman nobility), while also ensuring continuity between two popes. Gregory VII (r. 1073-1085), defender of the freedom of the Church, then sought to broaden the reform to bishops and priests by opposing lay investiture, a practice that was held responsible for the trade in ecclesiastical offices, henceforth condemned as "simony".
This drive unleashed the "Investiture Controversy" between the papacy and the Holy Roman Emperor, a crisis that was settled with the Concordat of Worms in 1122. Gradually, the papacy asserted its absolute jurisdiction (plenitudo potestatis) over the affairs of the entire Church (Latin / Western), while bishops exercised their authority solely within their diocese.
The reform was also aimed at the morals of the clergy: celibacy was imposed on all priests, and the duties of monks were extended to all the clergy. The Pope increasingly fulminated bulls, whose dissemination widened; he established papal legates in all countries of Western Christianity and began traveling. Ministry to the lay population was reinforced within the parishes, whose network was completed. From birth to death, the different stages were overseen by the Church. With the Lateran Council of 1215, the parish became the center of ministry; minimum attendance at the parish church by the faithful was set annually, at Easter, for confession and communion. Clerics advised the faithful to do good works, such as fasting and almsgiving, in order to redeem venial sins; penance was reserved for the most serious sins (capital or mortal).

Further remarks on the resources

Source 2:

The Church Militant, that is to say all Christians on earth fighting sin in their lifetime, is represented before a large church, probably the Cathedral of Santa Maria del Fiore (the Duomo of Florence), then under construction. Christian society is presented according to the Church’s vision. At the center of a row of seated figures is the Pope. To his left are three secular monarchs, who oversee the laity before them. To his right, the place of honor, is the spiritual clergy. Beside the Pope sit a cardinal (recognizable from his red hat), himself a Dominican, and a bishop. Before them, we recognize the different orders of the regular clergy: Benedictine (in black habit), Cistercian (white habit), Franciscan (brown habit), and Dominican (white habit and black cape), while the religious military orders are represented by a Hospitaller (black habit with white cross). The Pope holds a pastoral staff, and at his feet are the sheep who symbolize the people of God. They are guarded by dogs, whose black and white coats are emblematic of the Dominican order. They also evoke the play on words between Dominicani (Dominicans) and Domini canes (dogs of the Lord), in reference to their role of keeping followers in the true faith. Above this scene is the figure of St. Dominic showing the way of salvation, where Christians cleansed of sin enter the Triumphant Church in the afterlife.

Source 3 :

The clergy were to be released from the hold of the secular powers, as was later expressed in the phrase libertas Ecclesiae (freedom of the Church). Submission to the laity was seen as the root of the Church’s ills in the 11th century. Independence began with the first among the clergy, the Pope, whose election under the new regulations was entrusted to a college of cardinal-bishops. Outlawing simony, i.e., the purchase and sale of ecclesiastical ordinations and offices, had the same goal: clergymen were to be appointed based on suitability, not for the income they would derive. Prohibiting Nicolaism (clerical marriage) was essential in the drive to restore the moral discipline of the clergy. Reformers intended to set the clergy radically apart from the laity in their lifestyle, which was to be "apostolic", i.e., in imitation of the Apostles. In this sense, clerics were brought closer to the monks, being bound by chastity and the rules of communal life. Implicitly, papal authority was also being asserted, one that Nicolas II reminded was universal, extending to all Christendom.