Why are all these people going to Canterbury?
The shrine of St. Thomas a Becket was the destination for the pilgrims in Chaucer's Canterbury Tales. Becket was archbishop of Canterbury in 1170 and was martyred because of a disagreement with King Henry II. Henry made an off-hand wish that Becket would be killed, and four knights took him seriously and committed the deed in the north transept of Canterbury Cathedral. His body was placed in the crypt, and a few days later a series of miracles was said to have begun. Within two years the Pope had proclaimed Becket a saint. Canterbury became the most popular site for pilgrimages in England and one of the most popular in all Europe. Pilgrims would bring gifts and offerings, resulting in the cathedral becoming richly decorated. In addition, it was believed that special healing from sickness could be obtained by pilgrims who visited the shrine. That is why the General Prologue describes the reason of the pilgrimage as: "the holy blissful martyr for to seek that them hath helped when they were sick."
All the characters in Geoffrey Chaucer's "The Canterbury Tales" are headed to Canterbury for a pilgrimage. They are all going to visit the tomb of Saint Thomas a Becket.
Becket was killed in 1170 and was revered because he had been killed because of his devotion to the Church. He had made the king angry by not agreeing with him and taking the side of the Church instead and so the king (more or less) had him killed.
People in these times went on pilgrimages because they believed it would make them look better in God's eyes and improve their chances for a good afterlife.