In simple terms, the Protestant Reformation was a religious movement among those who sought to reform the Catholic church in the 16th century. When the church opposed them, there was a schism. Protestantism was born.
Some of the key players of the Protestant Reformation were Martin Luther, John Calvin, John Knox, and Ulrich Zwingli. These men differed from their Catholic counterparts in two ways.
First, these men differed in their theology. Chiefly they differed in how a person should be saved. They believed in scripture alone, faith alone, and grace alone. These were the three theological foundations in opposition to the traditionalism of the Catholic church.
Second, these men, particularly Martin Luther, differed in some of the practices of the Catholic church. For example, he decried the selling of indulgences. When John Tezel, a Catholic preacher came selling indulgences, Luther was appalled. Here is Tezel's jingle: "As soon as a coin in the coffer rings, a soul from purgatory springs."
As for how this movement was connected to the Renaissance, there was a saying among the Reformers, "ad fontes," which brought them back to the classical world by passing over the traditionalism of the Medieval Ages. In this way, the Reformation could be seen as a religious outflow of the Renaissance.