Irony occurs when events turn out the opposite of what is expected, while satire pokes fun at social problems.
Both the monk and the friar are supposed to live humble lives in service of others and in imitation of Christ. Ironically, they each do the opposite.
The monk is supposed be cloistered, which means to live in the monastery, apart from the world. Clearly, he is not doing that, since he is on the pilgrimage to Canterbury. Further, he leads a very comfortable life, more akin to what we might associate with the lord of the manor. His habit is trimmed with gray fur, a sign of wealth, and he is fat with a shining bald head and face, suggesting he is in robust, well-fed good health. We learn that:
Of priking and of hunting for the hare was al his lust, for no cost wolde he spare.
In other words, he spares no cost on his hunting for hares, which is his passion. He is also a womanizer, with a sweet, lisping voice he uses to woo the ladies, ironic since to become a monk he had to take vows of chastity—and also he should be inside his all-male monastery. The host points out that if had not been a monk, he would have "fathered dozens."
The friar is likewise a worldly rather than a religious man. The friar should be serving the poor, but, ironically, he is serving himself. We find that he is:
Ful wel biloved … with the worthy wommen of the town.
In other words, he is sleeping around. He has also benefitted financially from a scheme in which he has let out word that his penances for sin are easy. The rich people flock to him, but his easy penances come with a price tag that has made him quite financially comfortable.
Chaucer uses both these figures to satirize or poke fun at the corrupt state of the clergy and the church in his time period.