Simony (the selling of Church offices) and nepotism (favoritism based on family relationships) were rampant.
Clearly, if the Pope was concentrating on these worldly issues, there wasn't as much time left for caring for the souls of the faithful.
The corruption of the Church was well known, and several attempts had been made to reform the Church (notably by John Wyclif and Jan Hus), but none of these efforts successfully challenged Church practice until Martin Luther's actions in the early 1500s.
For example, Baptist is currently the largest denomination in the United States but there are many dozens more. Today, we call this "Roman Catholic" because there are so many other types of churches (for example, Methodist, Baptist, Lutheran, Calvinist, Anglican - you get the idea).
To understand the Protestant Reform movement, we need to go back in history to the early 16th century when there was only one church in Western Europe - what we would now call the Roman Catholic Church - under the leadership of the Pope in Rome.
So, if we go back to the year 1500, the Church (what we now call the Roman Catholic Church) was very powerful (politically and spiritually) in Western Europe (and in fact ruled over significant territory in Italy called the Papal States). There was the Holy Roman Empire (largely made up of German speaking regions ruled by princes, dukes and electors), the Italian city-states, England, as well as the increasingly unified nation states of France and Spain (among others).
The power of the rulers of these areas had increased in the previous century and many were anxious to take the opportunity offered by the Reformation to weaken the power of the papacy (the office of the Pope) and increase their own power in relation to the Church in Rome and other rulers.
Luther sparked the Reformation in 1517 by posting, at least according to tradition, his "95 Theses" on the door of the Castle Church in Wittenberg, Germany - these theses were a list of statements that expressed Luther's concerns about certain Church practices - largely the sale of indulgences, but they were based on Luther's deeper concerns with Church doctrine.
Before we go on, notice that the word Protestant contains the word "protest" and that reformation contains the word "reform"—this was an effort, at least at first, to protest some practices of the Catholic Church and to reform that Church.
The sale of indulgences was a practice where the church acknowledged a donation or other charitable work with a piece of paper (an indulgence), that certified that your soul would enter heaven more quickly by reducing your time in purgatory.
Keep in mind too, that for some time the Church had been seen as an institution plagued by internal power struggles (at one point in the late 1300s and 1400s, church was ruled by three Popes simultaneously).
Popes and Cardinals often lived more like kings than spiritual leaders.
Popes claimed temporal (political) as well as spiritual power.
They commanded armies, made political alliances and enemies, and, sometimes, even waged war.