The Catholic Counter-Reformation was a modestly successful movement to reform the church and end the division of Christianity. While they failed to reunite all of Christianity, they were mildly successful in reforming the church and bringing some people back to Catholicism.
The Catholic Pope controlled all of Catholicism, and in turn all or Europe until a man named Martin Luther came along. Martin Luther was unhappy with the abuses of the Catholic Church and decided to break away from the church. From the moment Luther broke away from the Catholic Church, religion was never the same. His break created a new sect of Christianity called Lutheranism and brought to light the abuses of the Catholic Church. Soon the Catholic Church began to loose members and they realized they had to do something. Fast.
In hopes of ending the schism that Luther had created, the Catholic Church decided to make some serious changes. These changes were labeled the Catholic Counter-Reformation, or simply the Catholic Reformation. During this reformation the acknowledged that many people turned away from the church because of the levels of corruption within it. They acknowledged that many clergy were taking advantage of their positions and others were so poorly educated they did not even understand their own sermons. They realized they had to address these issues and they created the Council of Trent to deal with them.
To deal with the issue of under education of clergy
The Council of Trent did a pretty original thing, they ordered that every diocese have a seminary to educate and train its clergy. The men who truly had a calling were chosen to become the priests. This made sure the priests were not only educated, but also that they truly wanted to serve God. To deal with the issue of pluralism (where men would serve as bishops in multiple diocese): the Council of Trent decreed that bishops must live in their own dioceses and visit every religious house within that diocese at least once every two years. To deal with the issues of priests having mistresses: the Council of Trent reaffirmed that having a mistress was against church doctrine.
In this matter the Catholic Church hoped that the Priests would realize their actions were not supported by the Catholic Church, and they would stop. To bring people back to the Catholic Church orders of deeply religious people, such as Jesuits, were created. These orders were made up of people willing to go to any length to re-convert people to Catholicism. While the above reforms were fairly successful, the Catholic Church refused to give in on matters of tradition and sacraments. This stubbornness cost them the reunification of the Catholic Church and Europe.