To “confess” something means to declare it; you can confess your sins, for example. You can also confess (“declare”) your faith or religious affiliation. When historians write about the formation of “confessions” during the age of Protestant Reformation and Catholic Renewal, they mean the “hardening of the diverging Christian faiths”—Catholic, Lutheran, Calvinist, etc.—“into more or less stable church[es]...with their own doctrines, constitutions, and religious and moral styles.” These “more or less stable churches” were ususally organized around an explicit statement of definitive beliefs, or doctrines. The mainstream Protestant faiths in Germany had such a document in the Augsburg Confession of 1530; the decrees of the Council of Trent (1545-1563) can also be seen as such an assertion.
They also mean a political process: in the sixteenth century, declaring your religion (your “confession”) was quite often the same thing as taking sides in a political struggle over the religious direction a town or lordship might take, and vice versa. Thus the formation of confessions is also about the emergence of political and military coalitions among religiously like-minded people, such as the Huguenots and the Catholic League in France or the Protestant League of Schmalkalden in Germany. It is important to bear in mind, however, that not everyone's opinion in these matters weighed equally. On the contrary, the legal precondition of all confessions was the idea that a sovereign possesses the authority to determine the religion of its subjects—which normally meant that princes and their councillors decided what confession would be adopted for the territories under their rule. These relationships were summarized in the legal coinage cuius regio, eius religio—“he who reigns establishes the religion.”
Many historians have taken this reality and built upon it a framework for understanding the development of religious belief and practice throughout the early modern period. For these historians, state-building is the key to understanding the pattern of change in religion. From this perspective, the sixteenth-century reformations, Protestant and Catholic alike, aimed at christianizing the European population at large—in other words, to bring popular religious belief and practice into conformity with the learned theologies and doctrines of the official churches. On the grand stage of cultural history, therefore, the sixteenth-century reformations had much more in common than set them apart. But reforming popular religion in this manner was far beyond the capacity of any church to accomplish on its own; furthermore, confessional division and conflict weakened the churches and diverted energies away from moral reform. To secure themselves against competitors, the major faiths forged alliances with the princes of Europe—and again, this was true of Catholicism as well as the Protestant confessions. The result was an unprecendented fusion of secular and spiritual powers, state and church. This, finally, goes a long way to explaining the politicization of religion in the sixteenth century: increasingly, adherence to a confession was simultaneously a matter of obedience to one's sovereign lord and ruler, and dissent by definition an act of rebellion against that authority.
Source: Ernst Walter Zeeden, “Grundlagen und Wege der Konfessionsbildung in Deutschland im Zeitalter der Glaubenskämpfe,” Historische Zeitschrift 185 (1958): 249-299; Wolfgang Reinhard, “Zwang zur Konfessionalisierung? Prolegomena zu einer Theorie des konfessionellen Zeitalters,” Zeitschrift für historische Forschung 10 (1983): 257-277.