There were a number of political and religious rivalries in Europe at this time that caused quite a bit of turmoil. Let's look at what caused some of the major ones.
There had been attempts to reform the Catholic Church going back to the fourteenth century. A number of early reformers were concerned with corruption amongst the clergy. For instance, the Bohemian priest Jan Hus was concerned with the vast wealth of the Church and spoke out criticizing the pope’s authority. In 1414, he was charged with heresy and executed. He and other early reformers inspired the German monk Martin Luther to challenge the Church's authority. He was particularly concerned with the sale of indulgences, which he saw as a corrupt money-making scheme. After he was forced out of the Church in 1521, Luther started his own denomination, known as Lutheranism.
Luther gained the support of a number of German princes who were unhappy with their position as subordinates to the Catholic leadership. A number of localized religious and political conflicts took place over the next three decades, as princes fought one another and the Catholic Church tried to reconsolidate power. These wars ended in 1555 with the signing of a treaty known as the Peace of Augsburg, which stated that each prince within the Holy Roman Empire could determine the religion of his particular principality.
As we can see, it was the struggle between princes that caused many of the divisions in Europe. Whether to remain Catholic or to adopt one of the new Protestant religions created much of the strife of this period. There were other divisions throughout Europe at this time with similar origins, namely King Henry VIII of England founding the Anglican Church. Like many of the German princes who adopted Lutheranism, King Henry also wanted independence to rule without the interference of the Catholic Church.