Why did some religious people want to reform the church during medieval times?

Answer 1

They became aware how powerful the influence of church is on the population, when the people started giving their money to the church. Lets not forget about confessions. This was powerful too knowing who is doing what and reporting to whoever was ruler or king.

Answer 2

Those people were called Reformers. The Reformers most famous today are Martin Luther and John Calvin. Luther alone posted 95 objections against Roman Catholic church practices and Calvin wrote several books on the subject, so you don't want me to go into great detail here.

Their main objection was that Christian belief should be based directly on what it says in The Bible, and not on what the Pope, bishops and priests gave you as their interpretation of the Bible (the art of printing just having been invented, most people never had seen a bible up close, let alone read it themselves). They objected also against many rules and teachings of the Roman Catholic church that had no basis at all in the Bible itself, like the existence and worshipping of the Saints and the Holy Virgin, the power of bishops and priests over the faithful and - especially in the case of Luther - celibacy of priests.