Pilgrimages were an important expression of religious feeling in Cadfael's day. Shrewsbury Abbey wanted the body of St. Winifred in order to attract more pilgrims. For general information on medieval pilgrimages, see Pilgrims and Pilgrimages -- the other pages on this site are also well worth exploring. (image of scallop shell from wikicommons licensed under GNU Free Documentation Licence)
Although we tend to think first of long distance pilgrimages to the Holy Land, Compostela, or Canterbury, local pilgrimages were also important, and this pdf article from Peregrinations explores the theme. The photobank of images at Peregrinations, the website for the International Society for the Study of Pilgrimage Art, is also well worth exploring. Here is a mosaic from Aachen cathedral to whet your appetite (photo by Asa Mittman via Peregrinations used by permission) .