It's very important to note that much of what was going on with the Jews throughout history also had to do with what was going on bigger picture with their countries of residence at the time. This was particularly true throughout the next six five or so centuries.
This time period was included in what was known as The Renaissance. This meant "rebirth" and represented a time where people began wanting to learn, and specifically around knowledge regarding the ancient times. People studied history, mathematics, philosophy, and much more.
What was going on with the Catholic Church is very important to understand. For a long time, this had been the power to be and had governed almost every part of daily life. At a certain point though, it began to way overstep its' bounds. The most negative aspect was widespread corruption, leading some to develop new opinions and ideas around what role religion really was meant to represent.
One of those people was Martin Luther. He observed what was happening with the church and decided to protest its' actions. He published his ninety-five theses and began to gain notice. His actions would lead to the spark of the new Protestant Reformation. Luther also saw how terrible the church had treated the Jews and came up with what he believed was a solution. His belief was that if he could just get the Jews to convert, that they would be able to engrain into society and all of their misfortune would vanish. When the Jews didn't comply with his plan, he felt completely rejected and became a huge antisemite. From there he wrote up his "honest advice" which outlined all the terrible ways the Jews would be treated moving forward. Hitler and the Nazis would later put this into action.
Jewish population was also expanding tremendously around this time in the areas of Ukraine. This area was being taken over by Poland and in order for the areas to function, they needed literate people who could help fill some of the important positions (Jews were the perfect candidates because they studied the Torah and could read/write). These positions included bankers, accountants, and people that could help keep the economy healthy.
As far as the Jewish religion and culture itself, it's important to note that during this century, something very important happened in the city of Tzfat (which at the time was the most populated Jewish city). Here the Kaballah was finally organized. This paved the way for Tzfat to be considered a very spiritual and holy place from this point onward.