Geoffrey Chaucer completed Canterbury Tales in the last decade of the 14th century. While there is no clear timeline, presumably, the story is developing during the same period. Chaucer uses it to comment on the most important topics of modern society. Basically, they are religion and the division of social classes.
Detailed answer:
Chaucer uses different characters to personify the challenges faced by Medieval society. The pilgrims represent different classes of society – the Knight, the Monk, the Physician, the Miller, etc. The only thing they have in common is their pilgrimage to the shrine of Thomas Becket in Canterbury. Chaucer uses different forms of storytelling, from parable to alchemical account. This helps him to reinforce the differences between the characters.
One of the main issues in late 14th century England was class conflict. Traditional feudal society was slowly falling apart. Less than half of able workers survived the Black Plague in the middle of the 14th century. It meant that the survivors could make their own rules because the demand for labor was extremely high. So, conflicts between landlords and peasants became very common. Characters like Miller and Reeve in Canterbury Tales represent the negative perception of the lower class.
English society was also becoming more secular due to different reasons. Firstly, the Black Plague seriously shook the foundations of faith. Secondly, the rise of secular education made the position of the clergy weaker. Lastly, the corruption within the Catholic church was all too evident. Chaucer demonstrates it through his portrayals of the Summoner, Pardoner, and Friar.