I have some expertise in this field, so I will attempt to answer as concisely as I can. When it was founded in 966, the medieval Polish state accepted Latin Christianity as its state confession. Until about 1340, Poland was a uniformly Latin (Catholic) Christian, uni-confessional state. When Kazimierz III (the Great) acquired Red Ruthenia, the medieval Polish state became bi-confessional, with a sizable Eastern (Orthodox) Christian population. This Eastern Christian population grew further when Poland and Lithuania entered a personal union in 1385. However, despite a politically powerful Eastern Christian noble faction, the Polish king and the Grand Duke of Lithuania were required to be Latin Christians.

This status-quo remained unaltered throughout the Early Modern period. When the Protestant Reformation swept through Europe, monarchs and dukes more than anyone decided on the dominant confession of their respective states (cujus regio, ejus religio). By the middle of the sixteenth century, the Polish-Lithuanian state was home to many converts to Lutheranism, Calvinism and later, Anti-Trinitarianism, which ranged from wealthy burghers to powerful magnates. Zygmunt II August, king of Poland from 1548-1551, himself flirted with Protestantism. His second wife, Barbara, came from the powerful Radziwiłł clan, many of which were ardent converts to Calvinism. Zygmunt even considered the creation of a national church, akin to Henry VIII's religious experiment. At the height of the Protestant tide, Protestant nobility were even able to insist that succeeding monarchs make an oath of tolerance to any residents of the Polish-Lithuanian state who dissented from the official state creed (the so-called Henrician Articles (1573), named after Henri Valois, Poland's first elective monarch). Zygmunt's successors complied, but simultaneously exerted a kind of soft power to promote Catholicism over dissenting confessions.

For example, Stefan (Istvan) Bathory (+1586) invited the Jesuits, who through preaching, teaching and polemics were able not only to turn back the tide of conversions, but were highly effective at winning many nobles back to the Catholic fold. Jesuit colleges were particularly effective tools of reconversion. Political participation in the Polish-Lithuanian Commonwealth required good knowledge of Latin, rhetoric and classical political texts. The Jesuits did not bring the Renaissance to Poland - but they taught! Protestant nobles frequently sent their sons to Jesuit schools because of the impeccable reputation these institutions possessed - and then were surprised when their sons returned home as ardent Catholics. Jesuit polemicists were likewise effective in fostering a cultural discourse in which to be Polish meant to be Catholic (see especially Piotr Skarga (SJ) "Parliamentary Sermons"). In a political environment where state-issued political offices meant social prestige, Polish kings tended to distribute them only to Catholics, providing yet another incentive to be on the "right side" of the confessional divide. Following the Council of Trent (1545-1563), the project of Catholic Reform offered a cohesive program of spiritual, moral and intellectual renewal. In the Polish-Lithuanian Commonwealth, "Protestantism" was never a cohesive movement. Lutherans tended to be urban and ethnically German. Calvinists were usually nobility, later themselves divided by the emergence of an Anti-Trinitarian faction. In 1596, the Jesuits engineered a confessional union with the Eastern (Orthodox) Church in the Commonwealth, the so-called Union of Brest. These Greek-rite Catholics were allowed to retain their rituals, married clergy and communion in both kinds - while recognizing the papacy.

Protestantism (in all its forms) and "dis-uniate" Orthodoxy (ie, those Orthodox who did not accept union with Rome at Brest) increasingly became confessions of "the other," especially after the 1655 so-called Swedish Flood, which witnessed an invasion by Swedish Lutheran troops as well as by Orthodox Cossacks and Muscovites, who were eager to loot Catholic sacred spaces. In the aftermath, many Protestant nobles were accused of being in cahoots with the invaders (viz. Janusz Radziwiłł), further "othering" non-Catholic confessions. Perhaps most crucially, Protestantism never managed to filter down to the peasantry, who remained overwhelmingly Catholic or Orthodox (and later, Greek-rite Catholic). In peasant discourse, Protestantism (broadly labeled as just "Lutheranism") remained a foreign creed, that of the Germans or Swedes, while post-Brest, Orthodoxy was the faith of the Muscovite. This narrative of Poles as Catholics continued to be perpetuated following the Partitions (post 1795), when the once-dominant state confession found itself under repeated pressure from Lutheran German and Russian Orthodox monarchs.

TLDR: The Polish monarchy (as all other Early Modern monarchies) was able to shape the confessional makeup of the state it ruled over (in this case, particularly through use of soft power). The cultural definition of what it meant to be "Polish" changed from one that was confessionally broad to one that was confessionally exclusive.

Some bibliography, with as much broadly accessible English-language scholarship as I can think of off the top of my head: Norman Davies, God's Playground: A History of Poland, Vol. 1: The Origins to 1795, New York: Columbia University Press, 2005; Borys Gudziak, Crisis and Reform: The Kyivan Metropolitanate, the Patriarchate of Constantinople, and the Genesis of the Union of Brest, Cambridge, MA: Harvard University Press, 2001; Janusz Tazbir, A State without Stakes: Polish Religious Toleration in the Sixteenth and Seventeenth Centuries, New York: Kościuszko Foundation Press, 1973; Jerzy Kłoczowski, A History of Polish Christianity, Cambridge, UK: Cambridge University Press, 2000; Ambroise Jobert, De Luther a Mohila: La Pologne dans la crise de la chretiente 1517-1648, Paris: 1974; Stanisław Litak, Od Reformacji do Oświecenia: Kościół katolicki w Polsce nowożytnej, Lublin: Towarzystwo Naukowe KUL, 1994; Kościół w Polsce. Tom I. Średniowiecze, Jerzy Kłoczowski, ed., Kraków: ZNAK, 1968; Kościół w Polsce: wiek XVI-XVIII, Tom II, Jerzy Kłoczowski, ed., Kraków: ZNAK, 1969.

New and additional answers to this question are encouraged, as this question has not been answered in-depth on AskHistorians so far. But if your question doesn't receive such an answer, you could have a look at this similiar prior discussion:

Why does the Czech Republic have so many atheists, yet Poland is so strongly Catholic?