The is a vague question, because Penelope deals with people in different ways. So, she has a different effect. For example, because of her beauty, the suitors desire her and want to marry here. Also she frustrates them, because she holds out by employing various techniques. She deals with her husband in a different way. She is faithful to him. There is another perspective. Penelope also has an effect on the reader. She is a model of faithfulness and character to the readers. This is especially true in a Greek context.
The most common description of Penelope is the word "circumspect." This indicates that she is careful, intelligent, and conscientious. Penelope's cleverness is a good match for her husband Odysseus's. Her awareness of the world around her is what sustains her and her household for twenty years after Odysseus leaves for the Trojan War.
When the suitors overrun the Ithaca palace, Penelope uses her wiles to hold them back as much as possible. They are continually angered by her techniques to halt them, but the fact that these tactics work in the first place says a lot about Penelope's resourcefulness. At the beginning of the epic, these tactics often exasperate her son Telemachus as well, because Telemachus does not believe that his father will return.
Another interesting complexity about Penelope is the fact that she is optimistic, and at the same time, extremely wary. She never lets go of the hope that her husband Odysseus is still alive and will return to Ithaca, even when their son Telemachus becomes pessimistic. However, her wariness often shows up as well. When Odysseus finally does return at the end, she plays a game with him to doubly make sure that it really is him. She knowingly tells Odysseus, who is disguised as a beggar, that she has moved their wedding bed. The real Odysseus would know that this is ridiculous, as their bed was carved from an olive tree that was still rooted to the ground (an apt metaphor for their marriage). He protests, and so Penelope gets her certainty that her husband really is back.