Why were The Canterbury Tales important in Geoffrey Chaucer's time, and why are they important now?

Geoffrey Chaucer's The Canterbury Tales is a vast and sweeping work that grapples with many important issues, so it's impossible to answer this question by providing all the reasons why the poem was and continues to be relevant. As such, my answer will involve my own particular interpretation, and you should be aware that other scholars might choose to focus on other important themes. For my part, however, I believe that the innovative interplay of social classes is what makes Chaucer's masterpiece stand out. 

The poem features the interaction of many different social groups and classes of people, from the high and mighty Knight to simple craftsmen, such as the Carpenter. By doing so, Chaucer illustrates a society striking in its diversity, and we're treated to multiple perspectives based on the social standing of different characters. This exploration of differing ideas and viewpoints would have been important in Chaucer's day, and it has only become more relevant in contemporary society. In a time when the middle class faces heavier financial burdens and the poor are becoming poorer and the rich more wealthy, it's important to remember that our society is composed of vast numbers of people from different walks of life. We do not need only the perspectives of the upper classes (which, in Chaucer's poem, would have been represented by the Knight). Instead, we need many different views from all members of society, including the perspectives of people like the Carpenter, the Weaver, the Yeoman and the Plowman, Chaucer's characters from more "humble" origins.