There are four typically recognized themes in Geoffrey Chaucer's The Canterbury Tales: Christianity, deception, spring, and reputation. Essentially, the reason that the tales continue to be recognized as important lies in the fact that modern readers can still relate to the work, 626 years after it was written.
While the theme of Christianity may not apply to all modern audiences, most people recognize it as a major religion and belief. Also, the theme of spring may not be one which all people recognize if they have not studied the rejuvenating and renewal aspects associated with it.
Outside of those, both deception and reputation are themes illustrated in the text which modern audiences can appreciate. Many people do not like those who act in deceptive ways. Given that we live in a society which judges people on their actions (as see historically), the idea of deception speaks to modern audiences. This theme will continue to speak to audiences given its universal appeal and timelessness.
Like deception, modern audiences understand reputation. As a culture which tends to make immediate judgements, the reputation of a person speaks highly of how those around them perceive them. Give that a reputation is created based upon a person's interpretation of another, the concept of reputation will never vanquish. Again, this is another theme which is both universal and timeless.