This morning I was asked about the Canterbury Tales. The question was questionable (perhaps I will write about that some other time) because of its wording and range. For the purposes of this answer, I am going to answer by understanding it as "Why should one read the Canterbury Tales today? "
The Canterbury Tales is a compilation of stories framed within a pilgrimage and a storytelling contest. Geoffrey Chaucer wrote it at the end of the 15th century but did not finish it.
Readers approaching the Tales might not realize how different it is from other medieval texts, but they will be given the opportunity to dive into the complexity of medieval society. In the Tales, Chaucer records not only diverse social classes and roles, but a nascent bourgeoisie that would eventually take over the medieval class structures.
That is not to say that the text is flat. The narrative and its contained stories are presented in contraposition with themselves in multiple layers of meaning. Chaucer, the narrator, describes aspects of the other pilgrims or their interactions with each other in such a way as to allow Chaucer, the author, or today's reader to form their own opinion of the pilgrims. In this way, the Knight is noble and straight but is likely to have fought as a mercenary in what the West is likely to perceive as the wrong side of the Crusades. The Prioress is not as refined (she doesn't know Paris' French), and her compassion, so acute in reference to her little dogs, seems lacking when other humans are involved. The Pardoner, the seemingly most immoral character from an Anglo-Protestant perspective, tells what is arguably the most moral story in the book. If one wants to understand medieval society, its complexities, its challenges, one should read the Canterbury Tales.
The moral and psychological complexities of the Pardoner are only one example of a non-stereotypical description of a literary character. If we think that today this is not unusual, we will do well to remember that medieval texts thrived on types and allegorical writings. To present characters closer to real people in their inner intricacy appears much closer to what we expect from our contemporary narratives. The Wife of Bath, for example, tells stories about her husbands, four of which were relatively decent to her and the last one, the one she truly loved, who was also her abuser. Anyone who doesn't understand why she might have still loved him despite the fact that he beat her in such a way as to leave her deaf in one ear does not have much knowledge about how an abusive relationship is constructed. If one wants to understand the human condition and how it was expressed in the past or how this illuminates the human condition today, one should read the Canterbury Tales.
There are many fabliaux (humorous and scatological tales with clear misogynistic tendencies), but very few like "The Miller's Tale," in which the woman gets to make the jokes, fart the farts, and come out of the story as the unscathed manipulator of the whole situation. This is not to say that there is no misogyny in the Canterbury Tales, but to show how the author plays with superimposing layers in which class, gender, and status are subverted at one point and reinforced at another. If one is interested in challenging humour, one should read the Canterbury Tales.
Within its frame, the Tales contains a multitude of genres. Fairy tales, moral tales, legends, remakes, fabliaux, sermons, and more are represented within this work. If one is interested in the making of literary genre, one should read the Canterbury Tales.
Each of the tellers relates to others and themselves through their narratives, i.e. the tale holds subtle clues regarding who is telling it. This is part of the complexity of the structure of the work (something with which Chaucer had played before in the Book of the Duchess, but that gets magnified and perfected in the Canterbury Tales. If one is interested in literary structure and the construction of narratives, one should read the Canterbury Tales.
In this book, Chaucer introduced the iambic pentameter in English, a decasyllabic verse with a pattern of non-stressed/stressed syllables (a heart rhythm) which was later used by Spencer and Shakespeare. If you are interested in poetry and its history, you should read the Canterbury Tales.
As I said above, there is a character in the Tales named Chaucer, although critics often separate him from Chaucer, the narrator. Chaucer, the character, represents a clever play with the boundaries of fiction. It brings us to a world of metatextuality, self-referentiality, and self-deprecating humour. If one is interested in authorial awareness, one should read the Canterbury Tales.
In the last few years, we have seen studies on the performative aspects of the Tales, and arguments have been put forward as to whether this work was meant to be performed. The CantApp emphasizes the potential of the spoken word (as Baba Brinkman has done with his Rap Canterbury Tales and his argument tracing rap to medieval times). If one is interested in theatre and performance, one should read the Canterbury Tales.
There is more to say, but these points should begin to answer the initial question. I see in the Canterbury Tales what I see in other great literary works like Joyce's Ulysses or García Márquez's One Hundred Years of Solitude, a layering of signifiers stuck around each other like the layers of an onion: it might not be possible to understand all of them, but they can contribute to our understanding of the human condition, the history of our language, and the refinement of our interpretive skills.