Medieval society was a dismal time in world history. Illiteracy and poverty were the norm. Corruption in both religion and politics was rampant. There was a burgeoning middle class of workers who ultimately led the way to social change.
The Black Plague and the Hundred Years War had decimated and demoralized the population. It had become tradition for anyone who could to make pilgrimages to great religious sites, in this case the cathedral at Canterbury where St. Thomas a Becket was entombed.
Thomas a Becket was the Archbishop at Canterbury under King Henry II. Originally favored by the king, Becket held to his religious convictions and was eventually assasinated by four of the king's knights in 1170. Over the next century, Becket was canonized and miracles of healing were attributed to him and to the shrine where he was interred.
People visit shrines of all kinds for many reasons: luck, sympathy, healing, status, and traddition just to name a few. Chaucer's pilgrims represent all kinds of people who made the trek to the cathedral in search of spiritual favor, miracles, and power.