It refers to the period of the so-called Avignon Papacy (1309 to 1377) during which seven successive Popes resided in Avignon in France rather than in Rome. This absence of the Popes from Rome is also sometimes called the “Babylonian Captivity of the Popes” or the “Babylonian Captivity of the Church” although we do not know when and where these expressions originated. Most probably they can be traced to Petrarch’s reference to Avignon as the “Babylon of the West” because of the worldliness of the Papal court there. It has nothing to do with Martin Luther’s thesis “On the Babylonian Captivity of the Church” which he published in 1520.
The situation arose from the conflict between the Papacy and the French Crown, involving Pope Boniface VIII and King Philip IV of France. It had further consequences like the Western Schism which dented the credibility of the Papacy seriously. End of Feudalism led to the rise of independent, autonomous nation states like, England, France, Germany, Spain, etc. which refused to accept the papacy as a transnational institution. But the Papacy refused to accept this new situation and continued to defend its supremacy using traditional theological and legal arguments. This was the cause of the rather violent conflict between the King of France Philip IV and Pope Boniface VIII. His election took place in an unusual manner. In order to put an end to the worldliness of the Papacy, the cardinals chose in 1294 an eighty five year old hermit as Pope, who chose the name Celestine V. After only five months he realized that he was not able to fulfill his responsibilities and so resigned and the next Pope elected was Boniface VIII, perhaps the most absolutist Pope in history. One of the proofs of his claim to absolute power was the Papal Bull Unam Sanctam (1302) in which he said that it was essential for every human being to be subject to the Roman Pontiff. With such claims he came into conflict with the King of France, Philip IV, also called Philip the Fair. Angered by the Pope’s various measures, in 1303 the King sent soldiers to arrest him at Anagni where he was staying, with the intention of bringing him to trial. He was arrested but was freed by the Italian soldiers but he died of this shock within a month, a broken man. It was later alleged that he had persuaded his predecessor Celestine to resign thereby preparing the way for his own election. His successor Benedict IX died after a year. At his death the cardinals who were divided into many factions agreed upon one thing, that the next Pope should not be a strong personality like Boniface VIII.
So they elected a French cardinal through the influence of the French King who took the name Clement V in 1305 and as a sign of gratitude, he decided to shift his residence to France and settle down in Avignon. Avignon was a papal property and many previous Popes used to stay there escaping the violent politics of Rome but it was for the first time that the Papacy was completely shifted to this place. From 1309 to 1377 the Papacy remained there, virtually under French control. This came to be called the Avignon Exile. All the Popes of the Avignon period were naturally Frenchmen and most of the cardinals and the curial officials too. Naturally, criticism came of corruption and nepotism and there was widespread feeling that the Papacy should return to its traditional city, Rome. Thus Gregory XI who was Pope from 1370 decided to go back to Rome, persuaded by two women saints, Catherine of Sienna and Bridget of Sweden in 1377. He died the next year. The Italians, fearing that another French Pope might prefer to go back to Avignon, forced the election of Urban VI, an Italian cardinal. The French cardinals denounced it as invalid, and elected Clement VII, a French cardinal, who took up residence in Avignon once again. Thus there were two Popes now, both claiming legitimacy and excommunicating each other. The whole Western Church was divided into two camps leading to the Western Schism, the longest lasting Papal schism in history.