The word "wiliest" comes from "wily," which refers to a very clever and cunning person. It can also imply some crafty or astute characteristic. In this case, the passage tells us that there is a very complicated and dangerous quest, and that only the most clever people will be able to overcome it.
The devotion and faithfulness that Penelope displays for her husband affect the plot of The Odyssey. Because she is upset over Odysseus's absence, she is often visited by Athena. Athena does not want her to suffer even more, which leads various characters, including Athena and Odysseus, to keep her in the dark about some topics. Moreover, her rejection of the suitors and her unyielding love are strong reasons for Odysseus to go back to her.
