The Canterbury Tales, most likely composed between 1387–1400 CE, are centered on the journey of 31 pilgrims (including the poet) to visit Canterbury Cathedral to pay homage Thomas a Becket, the archbishop murdered by Henry II. Each pilgrim represents a different occupation, rank, and personality type—in the aggregate, Chaucer presents us with a picture and analysis of English society in the Middle Ages, and his method, as the question implies, is to use both biting and gentle humor to point out the sometimes wide gap between what a pilgrim should be, given his or her occupation or rank, and what he or she actually is.
One of Chaucer's gently satiric portraits in the Prologue is of the Prioress Madame Eglantine , a rank just below that of Abbess in a convent, who is introduced as
There was also a Nun, a Prioresse,/Her way of smiling very simple and coy,/Her greatest oath was only "By St. Loy!" (ll. 122-24)
Chaucer's choice of Madame Eglantine's oath to St. Loy is not random. St. Loy, the English rendering of St. Eligius, is a Bishop of Noyon who was known for having been the goldsmith for several of the Merovingian kings in France and was a courtier with particularly fine manners and clothes. Only later in life did he become concerned with the poor. Madame Eglantine's choice of patron saint is consistent with her behavior, described as "a courtly kind of grace,/a stately bearing fitting to her place" (ll. 144-45). Later, we learn that she has a brooch, which is inscribed with the phrase "Amor vincit omnia," or love defeats all—a concept common in the doctrine of courtly love, not in the Church that the Prioress represents.
The gap between the ideal and the real is much wider when Chaucer exercises his humor on the Monk, who should be quietly contemplating salvation in a monastery or ministering to the sick in his parish, but instead is
... a good man to horse;/Greyhounds he had, as swift as birds, to course [to hunt with him]. (ll. 193-94)
Chaucer describes a monk who has the trappings and behavior of a wealthy landowner—a horse, greyhounds to hunt with—that are antithetical to his position in the Church, which calls for good works rather than good hunting.
The Monk not only engages in unseemly behavior, but he also wears clothes to which he is not entitled as part of the religious establishment, going so far as to close his hood with a "wrought-gold cunningly fashioned pin;/Into a lover's knot it seemed to pass" (ll. 200-01), an ornament that would be strictly forbidden by his order and made worse by its "lover's knot." Another telling sign that the Monk has abandoned his calling is in Chaucer's description of his head, which "was bald and shone like a looking- glass" (l. 203), another violation of his order which would have required a tonsure.
With few exceptions among the pilgrims—the Knight, the Clerk of Oxford, the Knight's Squire (son), the Franklin—Chaucer finds significant gaps between the ideal and real in the personalities of the pilgrims, gaps that he explores with both gentle humor and biting satire, and in this, Chaucer's portraits create a montage of England in the Middle Ages.